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mathematics
calculus 10th edition

Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions

In Exercises, find and evaluate the derivative of the function at the given point. f(x) = 3x + 1 4x - 3' (4,1)
In Exercises, find and evaluate the derivative of the function at the given point. 1 1 = 7/20 y csc 2x, TT 4'2,
In Exercises, find and evaluate the derivative of the function at the given point. y = csc 3x + cot 3x, (7/1 6
In Exercises find the second derivative of the function.y = (8x + 5)³
In Exercises, find the second derivative of the function. y 1 5x +1
In Exercises find the second derivative of the function.ƒ(x) = cot x
In Exercises find the second derivative of the function.y = sin² x
The temperature T (in degrees Fahrenheit) of food in a freezer iswhere t is the time in hours. Find the rate of change of T with respect to t at each of the following times.(a) t = 1(b) t = 3(c) t = 5 (d) t = 10 T = 700 t² + 4t + 10
The displacement from equilibrium of an object in harmonic motion on the end of a spring iswhere y is measured in feet and t is the time in seconds. Determine the position and velocity of the object when t = π/4. y= = 1 cos 8t 1 4 sin 8t
In Exercises find dy/dx by implicit differentiation.x² + y² = 64
In Exercises find dy/dx by implicit differentiation.x² + 4xy - y³ = 6
In Exercises find dy/dx by implicit differentiation.x³y - xy³ = 4
In Exercises find dy/dx by implicit differentiation. √xy = x - 4y
In Exercises find dy/dx by implicit differentiation.x sin y = y cos x
In Exercises find dy/dx by implicit differentiation.cos(x + y) = x
In Exercises find equations for the tangent line and the normal line to the graph of the equation at the given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the equation, the tangent line, and the normal line.x² + y² =
In Exercises find equations for the tangent line and the normal line to the graph of the equation at the given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the equation, the tangent line, and the normal line.x² - y² =
A point moves along the curve y = √x in such a way that the y-value is increasing at a rate of 2 units per second. At what rate is x changing for each of the following values?(a) x = 1/2(b) x = 1 (c) x = 4
All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface area changing when each edge is 6.5 centimeters?
A rotating beacon is located 1 kilometer off a straight shoreline (see figure). The beacon rotates at a rate of 3 revolutions per minute. How fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer down the shoreline? 0 1 km K km 3 rev min Not drawn
A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is 30° (see figure). The position of the sandbag is s(t) = 60 - 4.9t².Find the rate at which the shadow of the sandbag is travelingalong the ground when the sandbag is at a height of 35 meters.
In Exercises, find the derivative of the function. f(x)=√√√x² - 4x + 2
A ball is dropped from a height of 20 meters,12 meters away from the top of a 20-meter lamppost (see figure). The ball’s shadow, caused by the light at the top of the lamppost, is moving along the level ground. How fast is the shadow moving 1 second after the ball is released? 20 m 1-12
The table shows the numbers (in millions) of single women (never married) and married women m in the civilian work force in the United States for the years 2003 through 2010.(a) Use the regression capabilities of a graphing utility to find a model of the form m(s) = as3 + bs² + cs + d for the
Two circles of radius 4 are tangent to the graph of y² = 4x at the point (1, 2). Find equations of these two circles.
In Exercises find d²y/dx² implicitly in terms of x and y.x² - y² = 36
In exercises find the derivative of the trigonometric function. y || 3(1-sin x) 2 cos x
In Exercises, find the derivative of the function. y = sin(πx)²
In exercises find the derivative of the trigonometric function. h(x) = 1 X - 12 sec x
In Exercises find the acceleration of the specified object.Find the acceleration of the top of the ladder described in Exercise 21 when the base of the ladder is 7 feet from the wall.Data from in Exercise 21A ladder 25 feet long is leaning against the wall of a house (see figure). The base of the
In Exercises find d²y/dx² implicitly in terms of x and y.x²y - 4x = 5
In Exercises, find the derivative of the function.h(x) = sec x²
Describe the relationship between the rate of change of y and the rate of change of x in each expression. Assume all variables and derivatives are positive.(a)(b) dy * dt || 3 dx dt
In exercises find the derivative of the trigonometric function. 1 585 9 + 1/7 = (1)8
In exercises find the derivative of the trigonometric function. y = x + cotx
In Exercises find d²y/dx² implicitly in terms of x and y.x² + y² = 4
In Exercises, find the derivative of the function.g(x) = 5 tan 3x
A security camera is centered 50 feet above a 100-foot hallway (see figure). It is easiest to design the camera with a constant angular rate of rotation, but this results in recording the images of the surveillance area at a variable rate. So, it is desirable to design a system with a variable rate
In exercises find the derivative of the trigonometric function. f(x) = -x + tan x
(a) Use implicit differentiation to find an equation of the tangent line to the hyperbola(b) Show that the equation of the tangent line to the hyperbola x² 6 200 y² = 1 at (3,-2).
In Exercises find dy/dx implicitly and find the largest interval of the form - a < y < a or 0 < y < a such that y is a differentiable function of x. Write dy/dx as a function of x.cos y = x
(a) Use implicit differentiation to find an equation of the tangent line to the ellipse(b) Show that the equation of the tangent line to the ellipse 2 + y 8 = 1 at (1, 2).
In Exercises find the slope of the tangent line to the sine function at the origin. Compare this value with the number of complete cycles in the interval [0, 2π]. What can you conclude about the slope of thesine function sin ax at the origin?(a)(b) 2 1 y -2+ RIN y = sin x T 2π X
In Exercises find dy/dx implicitly and find the largest interval of the form - a < y < a or 0 < y < a such that y is a differentiable function of x. Write dy/dx as a function of x.tan y = x
In Exercises find the slope of the tangent line to the sine function at the origin. Compare this value with the number of complete cycles in the interval [0, 2π]. What can you conclude about the slope of the sine function sin ax at the origin?(a)(b) 2 y y = sin 3x ли -2. 2π X
In exercises find the derivative of the trigonometric function. f(x) = sin x x³
A patrol car is parked 50 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes angles of (a) θ = 30°(b) θ = 60° (c) θ = 70° with
An airplane is flying in still air with an airspeed of 275 miles per hour. The plane is climbing at an angle of 18°. Find the rate at which it is gaining altitude.
In exercises find the derivative of the trigonometric function. f(t) = cos t t
In Exercises find an equation of the tangent line to the graph at the given point.Kappa curve |y²(x² + y²) = 2x² -3-2 3 (1, 1) -2. -3- 2 3
In Exercises use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. 1 y = x² tan- X
A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water (see figure). At what rate is the angle θ between the line and the water changing when there is a total of 25 feet of line from the end of the rod to the water? 10 ft X 0 PR
In exercises find the derivative of the trigonometric function. f(0) = (0+1) cos 0
An airplane flies at an altitude of 5 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates at which the angle of elevation θ is changing when the angle is(a) θ = 30°(b) θ = 60° (c) θ = 75°
In Exercises use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. = y = COS TX + 1 X
In Exercises find an equation of the tangent line to the graph at the given point.Lemniscate 3(x² + y2)² = 100(x² - y²) y 6 4 2 -4 -6+ (4,2) -X
In Exercises find an equation of the tangent line to the graph at the given point.Astroid y 12 f -12+ x2/3+ y2/3=5 (8, 1) 12
In exercises find the derivative of the trigonometric function. f(t) = 1² sin t
In Exercises use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. I + x + 1 - x^^ =
In Exercises find the derivative of the algebraic function.c is a constant f(x): = c² - x² c² + x²¹
In Exercises find an equation of the tangent line to the graph at the given point.Cruciform x²y²-9x²-4y² = 0 4 (-4,2√3) ++ -6-4-2 -4 J +x 2 4 6
A balloon rises at a rate of 4 meters per second from a point on the ground 50 meters from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 50 meters above the ground.
Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to overcome the centrifugal force, the road is banked at an angle of magnitude θ from the horizontal (see figure). The banking angle must satisfy the equation rg tan θ = v², where v is the
In Exercises find an equation of the tangent line to the graph at the given point.Rotated ellipse 7x²-6√3xy + 13y2 - 16=0| y -3 3 2 -2 -3+ (√3,1) | x 23
In Exercises use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. y = 2x x + 1
In Exercises use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. y = I + x, X
In Exercises find the derivative of the algebraic function.c is a constant f(x) = x² + c² x² - C²¹ 2'
In Exercises find an equation of the tangent line to the graph at the given point.Rotated hyperbola -3 3 نرا 2 1 y [xy=1] (1, 1) 1 2 3
In Exercises use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. y = x+1 x2 + 1
In Exercises find the derivative of the algebraic function. f(x) = (x³ - x)(x² + 2)(x² + x − 1) -
The combined electrical resistance R of two resistors R1 and R2, connected in parallel, is given byWhere R, R1, and R2 are measured in ohms. R1 and R2 are increasing at rates of 1 and 1.5 ohms per second, respectively. At what rate is R changing when R1 = 50 ohms and R2 = 75 ohms? 1 R || 1
Using the graph of ƒ,(a) Determine whether dy/dt is positive or negativegiven that dx/dt is negative(b) Determinewhether dx/dt is positive or negative given thatdy/dt is positive(i)(ii) 4 2 1 y 1 f 2 3 4 X
When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the equation pV1.3 = k, where k is a constant. Find the relationship between the related rates dp/dt and dv/dt.
In Exercises find the derivative of the algebraic function. f(x) = (2x³ + 5x)(x − 3)(x + 2)
In Exercises find an equation of the tangent line to the graph at the given point.Circle (x+2)²+(y - 3)² = 37 10 8 6 4 2 -4-2 -4+ (4,4) ++ 46 +x
In Exercises find the derivative of the algebraic function. 2 g(x) = x²(² X 1 x + 1
In Exercises find an equation of the tangent line to the graph at the given point.Parabola 10 8 6 4 2 + -2 24 -4 -6 + (y - 3)² = 4(x-5) (6, 1) 2468 +x 14
In Exercises, find the derivative of the function. g(x) = 3x² - 23 2x + 3
In Exercises find the derivative of the algebraic function. f(x) 1 X x - 3 2-
In Exercises find the slope of the tangent line to the graph at the given point.Bifolium: (x² + y2)² = 4x²y Point: (1, 1) -2 - 1 2 -1 -2 y 12 > X
In Exercises, find the derivative of the function.g(x) = (2+ (x² + 1)4)³
In Exercises find the slope of the tangent line to the graph at the given point.Folium of Descartes: x³ + y³ - 6xy = 0 Point: (,) y 4 3 2- 1 -2 1 2 3 4 ➤X
In Exercises find the derivative of the algebraic function. h(s) = (s³ - 2)²
As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that is proportional to its surface area (S = 4πr²). Show that the radius of theraindrop decreases at a constant rate.
In Exercises find the derivative of the algebraic function. h(x) = (x² + 3)³
In Exercises find the slope of the tangent line to the graph at the given point.Cissoid: (4x)y² = x³ Point: (2, 2) y 2 1 -1 -2 2 3 X
In Exercises, find the derivative of the function.ƒ(x) = ((x² + 3)³ + x)²
In Exercises, find the derivative of the function. f(v) 1 - 2v 1 + v
In Exercises, find the derivative of the function. h (t) || 12 13 +2 2
In Exercises find the derivative of the algebraic function. f(x) = 3√x(√x + 3)
Repeat Exercise 29 for a man 6 feet tall walking at a rate of 5 feet per second toward a light that is 20 feet above the ground (see figure).Data from in Exercises 29A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground.(a) When he is 10 feet from
In Exercises find the derivative of the algebraic function. f(x) = = 3x - 1 - X
In Exercises find the slope of the tangent line to the graph at the given point.Witch of Agnesi: (x2 + 4)y = 8 Point: (2, 1) -2 -1 - 3 1 2
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. x cos y = 1, 2, 3
A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground (see figure).(a) When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?(b) When he is 10 feet from the base of the light, at what rate is the length of his
In Exercises, find the derivative of the function. y X x4 + 4
In Exercises, find the derivative of the function. g(x): || x + 5 x² + 2 2 2
In Exercises find dy/dx by implicit differentiation and evaluate the derivative at the given point. tan(x + y) = x, (0, 0)
For the baseball diamond in Exercise 27, suppose the player is running from first base to second base at a speed of 25 feet per second. Find the rate at which the distance from home plate is changing when the player is 20 feet from second base.Data from in Exercises 27A baseball diamond has the
A baseball diamond has the shape of a square with sides 90 feet long (see figure). A player running from second base to third base at a speed of 25 feet per second is 20 feet from third base. At what rate is the player’s distance s from home plate changing? 3rd O 90 ft 2nd O Home 1st

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