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mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Use a graph to explain the meaning of lim f(x) x-a - 00.
Use a graph to explain the meaning of lim f(x) = ∞. x→a
What is a vertical asymptote?
Assumeand ƒ (x) = g(x) whenever x ≠ 3. Evaluateif possible. lim g(x) = 4 x-3
For the following exercises, estimate the functional values and the limits from the graph of the function f provided in Figure 14. Figure 14 345 23 -5-4-3-2 2 3 4 5 XA III 32 654 y
For the following functions, find the equation of the tangent line to the curve at the given point x on the curve. f(x)=√x x=9
For the following exercises, use technology to evaluate the limit. Evaluate the limit by hand. At what value(s) of x is the function discontinuous? 4x7 x 1 lim f(x), where f(x) = x²-4
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 limits using algebraic techniques. lim h 0 (h+6)²36 h
For the following exercises, evaluate the limits algebraically. lim h→0 (h+ 3)²-9 h
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) = x²2²-9 x + 3 x - 9, -6, x -3
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) = x² - 4 x-2 , a = 2
For the following exercises, evaluate the limits algebraically. lim h→0 V5-h-V5 h
For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5 lim h→0 f(x+h)-f(x) h
For the following exercises, draw the graph of a function from the functional values and limits provided. lim_ f(x) = 2, lim = -3, lim f(x) = 5,f(0) = 1, 2- x → x 0 f(1) = 0
For the following exercises, assume two die are rolled. What is the probability of rolling a pair?
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) = 25 - x² > x²10x + 25 a=5
For the following exercises, evaluate the limits using algebraic techniques. lim x → 25 x² - 625 √x-5
For the following exercises, use the definition of a derivative to find the derivative of the given function at x = a.f(x) = 2x2 + 9x
For the following exercises, use the definition of derivative to calculate the derivative of each function.f(x) = 5π lim h→0 f(x+h)-f(x) h
For the following exercises, evaluate the limits using algebraic techniques. lim x → 1 -x²9x) x
For the following exercises, draw the graph of a function from the functional values and limits provided. lim f(x) = 0, lim f(x) = 5, lim f(x) = 0, ƒ(5) = 4, x x x f(3) does not exist.
For the following exercises, draw the graph of a function from the functional values and limits provided. lim f(x)=6, lim f(x) = -1, lim f(x) = 5, ƒ(4) = 6, x 4 x 6+ x 0 f(2)=6
For the following exercises, evaluate the limits algebraically. lim x 0 √3-x-√3 X V3
For the following exercises, evaluate the limits using algebraic techniques. lim x-4 7-V12x+1 x-4
For the following exercises, evaluate the limits algebraically. lim x 9 x²81 13-√x, X
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)= x³ - 9x x² + 11x + 24 a=-3
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, 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 average rate of change between the two points. (−2, 0) and (−4, 5)
For the following exercises, draw the graph of a function from the functional values and limits provided. lim¸ ƒ(x) = 2, lim_ƒ(x) = −2, lim f(x) = − 4, x x-3° ƒ(-3)=0, f(0) = 0
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 — 27 А3 x² - 3x -, a = 3
For the following exercises, evaluate the limits using algebraic techniques. lim x-3 1 3+x 3 + x
For the following exercises, evaluate the limits algebraically. lim x 1 *- Vx √x-x2² 1 1- Vx
For the following exercises, find the average rate of change between the two points. (4, −3) and (−2, −1)
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 at x = a. f(x) = -2 x-4 ;a=4
For the following exercises, draw the graph of a function from the functional values and limits provided. _lim_ f(x) = 7², _lim_ƒ(x) = 7, lim 2 x 1 f(n) = √2,ƒ(0) does not exist. lim_f(x) = 0,
For the following exercises, evaluate the limits algebraically. lim x 0 X 1+ 2x - 1/
For the following exercises, determine why the function f is discontinuous at a given point a on the graph. State which condition fails. x f(x) = a=0 |x|
For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after launch and is given by the function s(t). s(0)
For the following exercises, find the average rate of change between the two points. (0, 5) and (6, 5)
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 at x = a. f(x) = -2 (x-4)² ;a=4
For the following exercises, evaluate the limits algebraically. lim x² x-> 4 2 2x - 1
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) = 2x+2 x + 2 a=-2
For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after launch and is given by the function s(t). s(2)
For the following exercises, find the average rate of change between the two points.(7, −2) and (7, 10)
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0. f(x) = (1 + x)1/x
For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after launch and is given by the function s(t). s(2) -
For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after launch and is given by the function s(t). s′(2)
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 at x = a. f(x)= ;a=3 x²-x-6
For the following exercises, evaluate the limits algebraically. x³ - 64 16 lim x 4x²
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 polynomial functions, find the derivatives. f(x) = x3 + 1
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0. g (x) = (1 + x)2/x
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 at x = a. f(x)= 6x²23x + 20 4x² 25 -;
For the following exercises, evaluate the limits algebraically. lim x 2 x- - 2 x 2
For the following polynomial functions, find the derivatives. f(x) = −3x2 − 7x + 6
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 at x = a. f(x) = √x-3 9-x ;a=9
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.h(x) = (1 + x)3/x
For the following exercises, evaluate the limits algebraically. lim x 2¹ x-2 x 2
For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after launch and is given by the function s(t).s(t) = 0
For the following exercises, use technology to evaluate the limit. sin(x) lim x - 0 3x
For the following polynomial functions, find the derivatives.f(x) = 7x2
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.i(x) = (1 + x)4/x
For the following exercises, evaluate the limits algebraically. |x - 21 lim x 2 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 technology to evaluate the limit. lim x 0 tan²(x) 2x
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.j(x) = (1 + x)5/x
For the following exercises, use a graphing calculator to determine the limit to 5 decimal places as x approaches 0.Based on the pattern you observed in the exercises above, make a conjecture as to
For the following polynomial functions, find the derivatives.f(x) = 3x3 + 2x2 + x − 26
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, 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 technology to evaluate the limit. lim x → 0 sin(x) (1 - cos(x)) 2x²
For the following exercises, use a graphing utility to find graphical evidence to determine the left- and right-hand limits of the function given as x approaches a. If the function has a limit as x
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) = x2 − 2x
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): = x² - 2x - 15 x-5
For the following exercises, evaluate the limits algebraically. |x - 4| lim x-4 4-x
For the following functions, find the equation of the tangent line to the curve at the given point x on the curve. f(x) = 2x2 − 3x x = 3
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) = x² - 2x x² - 4x
For the following exercises, evaluate the limits algebraically. |x - 4 lim x 4+ 4 x
For the following functions, find the equation of the tangent line to the curve at the given point x on the curve. f(x) = x3 + 1 x = 2
For the following exercises, use a graphing utility to find graphical evidence to determine the left- and right-hand limits of the function given as x approaches a. If the function has a limit as x
For the following exercises, evaluate the limits algebraically. |x - 4| lim x-4 4-x
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 function whose graph appears in Figure 3.Find the average rate of change of the function from x = 1 to x = 3. -5-4-3-2-1 y 3- II Figure 3 3 4 5 x
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)= = x3 x³ -
<p style="text-align: justify;">For the following exercises, determine where the given function f(x) is continuous. Where it is not continuous, state which conditions fail, and
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, consider the function whose graph appears in Figure 3.Find all values of x at which f′(x) = 0. -5-4-3-2-1 10 -3 5 # Figure 3 3 4 5 II # x
For the following exercise, find k such that the given line is tangent to the graph of the function. f(x) = x2 − kx, y = 4x − 9
For the following exercises, evaluate the limits algebraically. lim x 2 -8 + 6x - x² 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, 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 x²-3x - 10
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable. y 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 exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable. TI y x
For the following exercises, consider the function whose graph appears in Figure 3.Find all values of x at which f′(x) does not exist. -4-3-2-1 -5 3- -4- תי 5 ITIC + 3 4 5 IIII. Figure 3 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

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