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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises, find the derivative of the function. y = √x² + 1
In Exercises find the derivative of the algebraic function. f(x) = x41 2 x + 1
In Exercises find the derivative of the algebraic function. x + 3 4 I x = (x) f
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. x3 + y3 = 6ху — 1, (2, 3)
An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna (see figure). When the plane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane? K 5 mi X X Not drawn to scale
In Exercises, find the derivative of the function. y = zx²/16 − x2
In Exercises find the derivative of the algebraic function. f(x) = r2 +5x+6 x² - 4 X
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. (x + y)² = x³ + y³, (-1, 1)
In Exercises, find the derivative of the function. y=x√√1-x²
In Exercises find the derivative of the algebraic function. f(x) = 4- 3x - x² x² 1
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. x2/3 + y2/3 = 5, (8, 1)
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. y² || x² - 49 x² + 49' (7,0)
In Exercises complete the table to find the derivative of the function without using the Quotient Rule. Function 2x Xx1/3 y = Rewrite Differentiate Simplify
In Exercises complete the table to find the derivative of the function without using the Quotient Rule. Function 4x3/2 y X Rewrite Differentiate Simplify
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. y³x²= 4, (2, 2)
In Exercises, find the derivative of the function.ƒ(x) = x(2x - 5)³
A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of -0.2 meter per second. Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 6.
In Exercises, find the derivative of the function. g(t) = 1 √1²-2
A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.15
In Exercises complete the table to find the derivative of the function without using the Quotient Rule. Function 10 3x3 y Rewrite Differentiate Simplify
In Exercises, find the derivative of the function.ƒ(x) = x²(x - 2)4
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. ху = 6, (-6,-1)
In Exercises, find the derivative of the function. y || 1 3x + 5
A ladder 25 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 2 feet per second.(a) How fast is the top of the ladder moving down the wall when its base is 7 feet, 15 feet, and 24 feet from the wall?(b) Consider the
In Exercises complete the table to find the derivative of the function without using the Quotient Rule. Function y 5x2 – 3 4 Rewrite Differentiate Simplify
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(a) Water is being pumped into the trough at 2 cubic feet per minute. How fast is the water level rising when the depth h is 1 foot?(b) The water is rising at a rate of 3/8
In Exercises complete the table to find the derivative of the function without using the Quotient Rule. Function 6 7.x² y = Rewrite Differentiate Simplify
In Exercises (a) Find two explicit functions by solving the equation for y in terms of x.(b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. (c) Differentiate the explicit functions, and (d) find dy/dx implicitly and show that the result
In Exercises, find the derivative of the function. 3 (t - 2)4
In Exercises, find the derivative of the function. f(t) = 1 t-3, 2
In Exercises (a) Find two explicit functions by solving the equation for y in terms of x.(b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. (c) Differentiate the explicit functions, and (d) find dy/dx implicitly and show that the result
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end (see figure). Water is being pumped into the pool at 1/4 cubic meter per minute, and there is 1 meter of water at the deep end.(a) What percent of the pool is filled?(b) At what rate
In Exercises (a) Find two explicit functions by solving the equation for y in terms of x.(b) Sketch the graph of the equation and label the parts given by the corresponding explicit functions. (c) Differentiate the explicit functions, and (d) find dy/dx implicitly and show that the result
In Exercises complete the table to find the derivative of the function without using the Quotient Rule. Function y x² + 3x 7 Rewrite Differentiate Simplify
In Exercises, find the derivative of the function. y = 1 x-2
In Exercises, find the derivative of the function. s(t) = 1 4-5t-t²
In Exercises (a) Find two explicit functions by solving theequation for y in terms of x.(b) Sketch the graph of theequation and label the parts given by the corresponding explicitfunctions. (c) Differentiate the explicit functions, and (d) finddy/dx implicitly and show that the result is
In Exercises find ƒ'(x) and ƒ'(c). Function f(x) = sin x X Value of c TT 6 C
In Exercises, find the derivative of the function. f(x) = 3/12x5
A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 10 cubic feet per minute. Find the rate of change of the depth of the water when the water is 8 feet deep.
In Exercises find ƒ'(x) and ƒ'(c). Function f(x) = X COS X Value of c C TT 4
In Exercises find ƒ'(x) and ƒ'(c). Function f(x) = x - 4 x + 4 Value of c c = 3
In Exercises, find the derivative of the function. y = 24/9-x²
In Exercises find dy/dx by implicit differentiation. x = sec 1 y
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 15 feet high?
All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface area changing when each edge is (a) 2 centimeters(b) 10 centimeters
In Exercises find ƒ'(x) and ƒ'(c). Function f(x) = = x² - 4 x - 3 Value of c c = 1
All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is (a) 2 centimeters (b) 10 centimeters
In Exercises find ƒ'(x) and ƒ'(c). Function y = (x²-3x + 2)(x³ + 1) Value of c c=2
In Exercises find dy/dx by implicit differentiation.y = sin xy
In Exercises, find the derivative of the function. y = 3/6x² + 1
In Exercises, find the derivative of the function. g(x) /4 - 3x²
A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is(a) 30 centimeters (b) 60 centimeters
In Exercises find ƒ'(x) and ƒ'(c). Function f(x) = (x³ + 4x)(3x² + 2x - 5) Value of c C = 0
In Exercises find dy/dx by implicit differentiation.cot y = x - y
In Exercises, find the derivative of the function. f(t) = √√5 - t
The radius r of a sphere is increasing at a rate of 3 inches per minute.(a) Find the rates of change of the volume when r = 9 inches and r = 36 inches.(b) Explain why the rate of change of the volume of the sphereis not constant even though dr/dt is constant.
In Exercises use the quotient Rule to find the derivative of the function. f(t) = cos t 13
In Exercises find dy/dx by implicit differentiation.sin x = x(1+tan y)
The included angle of the two sides of constant equal lengths s of an isosceles triangle is θ.(a) Show that the area of the triangle is given by A = 1/2 s² sin θ.(b) The angle θ is increasing at the rate of 1/2 radian per minute. Find the rates of change of the area when θ = π/6 and θ =
In Exercises use the quotient Rule to find the derivative of the function. g(x) = sin x zr
In Exercises find dy/dx by implicit differentiation. (sin πx + cos πy)² = 2
In Exercises use the quotient Rule to find the derivative of the function. f(x) = X² 2√x + 1
The radius r of a circle is increasing at a rate of 4 centimeters per minute. Find the rates of change of the area when (a) r = 8 centimeters (b) r = 32 centimeters
In Exercises find dy/dx by implicit differentiation.sin x + 2 cos 2y = 1
In Exercises, find the derivative of the function.ƒ(t) = (9t + 2)2/3
In Exercises use the quotient Rule to find the derivative of the function. h(x)= || = √√√x x³ + 1 -3
In your own words, state the guidelines for solving related-rate problems.
In Exercises find dy/dx by implicit differentiation.4 cos x sin y = 1
In Exercises find dy/dx by implicit differentiation.x³ - 3x²y + 2xy² = 12
In Exercises a point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x.(a)(b)(c) dx y = cos x; dt 4 centimeters per second
In Exercises use the quotient Rule to find the derivative of the function. g(t) = 31² - 1 2t + 5
In Exercises a point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x.(a)(b)(c) x = 0 dx y = tan x; dt 3 feet per second
In Exercises find dy/dx by implicit differentiation.√xy = x²y + 1
In Exercises complete the table. y = f(g(x)) 5x 2 y = sin u = g(x) y = f(u)
In Exercises use the quotient Rule to find the derivative of the function. I + zx Xx = f(x)
In Exercises find dy/dx by implicit differentiation.x³y³ - y = x
In Exercises complete the table. y = f(g(x)) csc ³ x y = u = g(x) y = f(u)
In Exercises a point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x.(a) x = - 1(b) x = 0(c) x = 1 y = 2x² + 1; dx dt 2 centimeters per second
In Exercises a point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given values of x.(a) x = -2(b) x = 0(c) x = 2 1 dx 1 + x²¹ dt 6 inches per second
In Exercises assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. Equation x² + y² = 25 (a) (b) Find dy dt dx dt when x = 3, y = 4 when x = 4, y = 3 Given dx dt dy dt = 8 = -2
In Exercises complete the table. y = f(g(x)) y = 3 tan(x²) u = g(x) y = f(u)
In Exercises find dy/dx by implicit differentiation.x²y + y²x = -2
In Exercises complete the table. y = f(g(x)) y = √√√x³7 - u = g(x) y = f(u)
In Exercises find dy/dx by implicit differentiation.x³ - xy + y² = 7
In Exercises assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. Equation xy = 4 (a) (b) Find dy dt dx dt when x = 8 when x = 1 Given dx dt dy dt = 10 = 6
In Exercises find dy/dx by implicit differentiation.2x³ + 3y³ = 64
In Exercises find dy/dx by implicit differentiation.x1/2 + y¹/² + y = 16
In Exercises complete the table. y = f(g(x)) y = (5x-8)4 u = g(x) y = f(u)
In Exercises complete the table. y = f(g(x)) y = 1 √x + 1 u = g(x) y = f(u)
In Exercises assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. Equation y = 3x² - 5x (a) (b) Find dy dt dx dt when x = 3 when x = 2 Given dx dt dy dt = 2 = 4
In Exercises find dy/dx by implicit differentiation.x² - y² = 25
In Exercises assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. Equation y = √√√√x (a) (b) Find dy dt dx dt when x = 4 when x = 25 Given dx | dt dy dt = 3 = 2
In Exercises find dy/dx by implicit differentiation.x² + y² = 9
In Exercises(a) Find an equation of the tangent line to the graph of ƒ at the given point (b) Use a graphing utility to graph the function and its tangent line at the point (c) Use the derivative feature of a graphing utility to confirm your results. f(x) = x + 3 x - 3' (4,7)
In Exercises find the points at which the graph of the equation has a vertical or horizontal tangent line. 25x² + 16y² + 200x160y + 400 = 0
In Exercises determine the point(s) at which the graph of the function has a horizontal tangent line. f(x) = x² x - 1
In Exercises determine the point(s) at which the graph of the function has a horizontal tangent line. f(x) = x² x² + 1
In Exercises find and evaluate the derivative of the function at the given point. Use a graphing utility to verify your result. y X + COS X, πT 2 2 T
In Exercises(a) Find an equation of the tangent line to the graphoff at the given point(b) Use a graphing utility to graph thefunction and its tangent line at the point f(x) = 2x²-7, (4, 5)
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