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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

For the following exercise, use the given information to evaluate the limits: lim f(x) = 3, lim g(x) = 5
For the following exercises, consider the function whose graph appears in Figure 3.Find an equation of the tangent line to the graph of f the indicated point: f(x) = 3x2 − 2x − 6, x = − 2
For the following exercises, determine where the given function f(x) is continuous. Where it is not continuous, state which conditions fail, and classify any discontinuities. f(x)= = x+2 x³ + 8
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiableot differentiable. y NH H
For the following exercise, use the given information to evaluate the limits: lim f(x) = 3, lim g(x) = 5
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable. x
For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the function near x = a. Round answers to two decimal
For the following exercise, use the given information to evaluate the limits: lim f(x) = 3, lim g(x) = 5
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is
For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the function near x = a. Round answers to two decimal
For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the function near x = a. Round answers to two decimal
For the following exercises, evaluate the following limits. lim cos(x) x-2
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f(−1)
For the following exercises, find the derivative of each of the functions using the definition: f(x) = 2x − 8 lim h→0 f(x+h)-f(x) h
For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the function near x = a. Round answers to two decimal
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is
For the following exercises, evaluate the following limits. lim sin(x) x → 2
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f(0) -6-5-4-3-2-1 III y -4- 3 -6- -7+ 8- 10+ 2 3
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f(1)
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is
For the following exercises, find the derivative of each of the functions using the definition: f(x) = 4x2 − 7 lim h→0 f(x+h)-f(x) h
For the following exercises, evaluate the following limits. lim sin x 2 TT X
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f(2) 6-5-4-3-2- -5- 4- 2- 7 8- 1₂ I 40- Figure
For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the function near x = a. Round answers to two decimal
For the following exercises, refer to Figure 15. Each square represents one square unit. For each value of a, determine which of the three conditions of continuity are satisfied at x = a and which
For the following exercises, find the derivative of each of the functions using the definition: lim h→0 f(x+h)-f(x) h
For the following exercises, evaluate the following limits. f(x)= ) = [2x²+2x+1, x - 3, x ≤0 ; lim f(x) x>0²x=40+²
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f(3) -4- 3- -6-5-4-3-2-1 y ننا -8- f(x) 1 2 3
For the following exercises, use numerical evidence to determine whether the limit exists at x = a. If not, describe the behavior of the graph of the function near x = a. Round answers to two decimal
For the following exercises, find the derivative of the function. f(x) = 4x − 6
For the following exercises, refer to Figure 15. Each square represents one square unit. For each value of a, determine which of the three conditions of continuity are satisfied at x = a and which
For the following exercises, evaluate the following limits. 2x²+2x+1, (x - 3, f(x)=₁ x≤0 x>0 x 0 ; lim_ f(x)
For the following exercises, find the derivative of each of the functions using the definition: lim h→0 f(x+h)-f(x) h
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f′(−1) Figure 20 L LLLL ∞ ∞
For the following exercises, find the derivative of the function. f(x) = 5x2 − 3x
For the following exercises, use a calculator to estimate the limit by preparing a table of values. If there is no limit, describe the behavior of the function as x approaches the given value.
For the following exercises, refer to Figure 15. Each square represents one square unit. For each value of a, determine which of the three conditions of continuity are satisfied at x = a and which
For the following exercises, find the derivative of each of the functions using the definition: lim h→0 f(x+h)-f(x) h
For the following exercises, evaluate the following limits. f(x) = 2x² + 2x + 1, x < 0 (x - 3, ; lim f(x) x>0 x 0
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f′(0)
For the following exercises, use a calculator to estimate the limit by preparing a table of values. If there is no limit, describe the behavior of the function as x approaches the given value.
For the following exercises, find the derivative of each of the functions using the definition: f(x) = −x3 + 1 lim h→0 f(x+h)-f(x) h
For the following exercises, evaluate the following limits. lim x 4 Vx+5-3 x-4
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f′(1) 6-5-4-3-2-1 4 3- -2₂ Es ∞0 -8- II 1
For the following exercises, use a graphing utility to graph the function f(x) = sin (12π/x) as in Figure 16. Set the x-axis a short distance before and after 0 to illustrate the point of
For the following exercises, use a calculator to estimate the limit by preparing a table of values. If there is no limit, describe the behavior of the function as x approaches the given value.
For the following exercises, use a graphing utility to graph the function f(x) = sin (12π/x) as in Figure 16. Set the x-axis a short distance before and after 0 to illustrate the point of
For the following exercises, find the derivative of the function.Find the equation of the tangent line to the graph of f(x) at the indicated x value. f(x) = −x3 + 4x; x = 2.
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f′(2) -6-5-4-3-2-1 y 3- 21 45 -7- C f(x) 2 3 4
For the following exercises, find the derivative of each of the functions using the definition: f(x) = x2 + x3 lim h→0 f(x+h)-f(x) h
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, evaluate the following limits. lim (2x-[x]) x → 2+
For the following exercises, with the aid of a graphing utility, explain why the function is not differentiable everywhere on its domain. Specify the points where the function is not
For the following exercises, find the derivative of each of the functions using the definition: lim h0 f(x+h)-f(x) h
For the following exercises, evaluate the following limits. Vx+7-3 lim x 2 x²-x-2
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.f′(3) y -3- 6-5-4-3-2-1 5 -6 [I] f(x) -8 1 2 3
For the following exercises, use a graphing utility to graph the function f(x) = sin (12π/x) as in Figure 16. Set the x-axis a short distance before and after 0 to illustrate the point of
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, with the aid of a graphing utility, explain why the function is not differentiable everywhere on its domain. Specify the points where the function is not differentiable.
For the following exercises, use a graphing utility to graph the function f(x) = sin (12π/x) as in Figure 16. Set the x-axis a short distance before and after 0 to illustrate the point of
For the following exercises, consider the function shown in Figure 17.At what x-coordinates is the function discontinuous? SETE in Figure 17 # 3 4 5
For the following exercises, evaluate the following limits. x lim x 3 x-9
For the following exercises, use Figure 20 to estimate either the function at a given value of x or the derivative at a given value of x, as indicated.Sketch the function based on the information
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, consider the function shown in Figure 17.What condition of continuity is violated at these points? -445 2. 01 03 3 P 10 y Figure 17 x
Consider the function shown in Figure 18. At what x-coordinates is the function discontinuous? What condition(s) of continuity were violated? Figure 18
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, explain the notation in words. The volume f(t) of a tank of gasoline, in gallons, t minutes after noon. f(0) = 600
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, explain the notation in words. The volume f(t) of a tank of gasoline, in gallons, t minutes after noon. f′(30) = −20
Construct a function that passes through the origin with a constant slope of 1, with removable discontinuities at x = −7 and x = 1.
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, explain the notation in words. The volume f(t) of a tank of gasoline, in gallons, t minutes after noon. f(30) = 0
For the following exercises, explain the notation in words. The volume f(t) of a tank of gasoline, in gallons, t minutes after noon.f′(200) = 30
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
The graph of f(x) = sin(2x)/x is shown in Figure 20. Is the function f(x) continuous at x = 0? Why or why not? s 2:5 -45-4-35-325-215-1-0,5 40:5+ N 051525 Figure 20 35 4 45
For the following exercises, explain the notation in words. The volume f(t) of a tank of gasoline, in gallons, t minutes after noon.f(240) = 500
For the following exercises, explain the functions in words. The height, s, of a projectile after t seconds is given by s(t) = −16t2 + 80t.s(2) = 96
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, use a graphing utility to find numerical or graphical evidence to determine the left and right-hand limits of the function given as x approaches a. If the function has a
For the following exercises, explain the functions in words. The height, s, of a projectile after t seconds is given by s(t) = −16t2 + 80t.s′(2) = 16
For the following exercises, explain the functions in words. The height, s, of a projectile after t seconds is given by s(t) = −16t2 + 80t.s(3) = 96
For the following exercises, explain the functions in words. The height, s, of a projectile after t seconds is given by s(t) = −16t2 + 80t.s′(3) = −16
For the following exercises, explain the functions in words. The height, s, of a projectile after t seconds is given by s(t) = −16t2 + 80t.s(0) = 0, s(5) = 0.
For the following exercises, the volume V of a sphere with respect to its radius r is given by V = 4/3πr3.Find the average rate of change of V as r changes from 1 cm to 2 cm.
For the following exercises, the volume V of a sphere with respect to its radius r is given by V = 4/3πr3.Find the instantaneous rate of change of V when r = 3 cm.
For the following exercises, find the average rate of change The height of a projectile is given by s(t) = −64t2 + 192t Find the average rate of change of the height from t = 1 second to t = 1.5
For the following exercises, the revenue generated by selling x items is given by R(x) = 2x2 + 10x.Find the average change of the revenue function as x changes from x = 10 to x = 20.
For the following exercises, the revenue generated by selling x items is given by R(x) = 2x2 + 10x.Find R′(10) and interpret.
For the following exercises, the revenue generated by selling x items is given by R(x) = 2x2 + 10x.Find R′(15) and interpret. Compare R′(15) to R′(10), and explain the difference.
For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000. Find the average rate of change in the total cost as x changes from x = 10
For the following exercises, use the definition for the derivative at a point to find the derivative of the functions.f(x) = −x2 + 4x + 7 x = a, lim x→a f(x) - f(a) x - a
For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000.Find the approximate marginal cost, when 15 cellphones have been produced, of
For the following exercises, use the definition for the derivative at a point to find the derivative of the functions.f(x) = 5x2 − x + 4 x = a, lim x→a f(x) - f(a) x - a
For the following exercises, the cost of producing x cellphones is described by the function C(x) = x2 − 4x + 1000.Find the approximate marginal cost, when 20 cellphones have been produced, of
For the following exercises, use the definition for the derivative at a point to find the derivative of the functions.f(x) = −4/3 − x2 x = a, lim x→a f(x) - f(a) x - a
For the following exercises, determine why the function f is discontinuous at a given point a on the graph. State which condition fails. _f(x) = X, 2x, x = 3 x=3 a=3

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