 4.10.1: Find the most general antiderivative of the function. f (Check your...
 4.10.2: Find the most general antiderivative of the function. f (Check your...
 4.10.3: Find the most general antiderivative of the function. f (Check your...
 4.10.4: Find the most general antiderivative of the function. f (Check your...
 4.10.5: Find the most general antiderivative of the function. f (Check your...
 4.10.6: Find the most general antiderivative of the function. f (Check your...
 4.10.7: Find the most general antiderivative of the function. f (Check your...
 4.10.8: Find the most general antiderivative of the function. f (Check your...
 4.10.9: Find the most general antiderivative of the function. f (Check your...
 4.10.10: Find the most general antiderivative of the function. f (Check your...
 4.10.11: Find the most general antiderivative of the function. f (Check your...
 4.10.12: Find the most general antiderivative of the function. f (Check your...
 4.10.13: Find the most general antiderivative of the function. f (Check your...
 4.10.14: Find the most general antiderivative of the function. f (Check your...
 4.10.15: Find the most general antiderivative of the function. f (Check your...
 4.10.16: Find the most general antiderivative of the function. f (Check your...
 4.10.17: Find the antiderivative of that satisfies the given condition. Chec...
 4.10.18: Find the antiderivative of that satisfies the given condition. Chec...
 4.10.19: Find f.f x 6x 12x 2 19
 4.10.20: Find f.f x 2 x 3 x 6 f
 4.10.21: Find f.f x 1 x f
 4.10.22: Find f.f x cos x 4
 4.10.23: Find f.f t e f
 4.10.24: Find f.f t t st
 4.10.25: Find f.f x 1 6x, f 0 8 f
 4.10.26: Find f.f x 8x 3 12x 3, f1 6 f
 4.10.27: Find f.f x sx6 5x f 1 10 f
 4.10.28: Find f.f x 2x 3x x 0 0 f 1 3 4f
 4.10.29: Find f.f t 2 cos t sec 2 t 2 f 3 4 2 t f
 4.10.30: Find f.f x 3x f1 f1 0 2 f
 4.10.31: Find f.f x 2x, x 0, f 1 7 f
 4.10.32: Find f.f x 4s1 x 2 ,
 4.10.33: Find f.f x 24x f 1 5 f1 3 2 2x 10 f x
 4.10.34: Find f.f x 4 6x 40x f0 2 f 0 1 3 f
 4.10.35: Find f.f sin cos f 0 3 f 0 4 f
 4.10.36: Find f.f t 3st f4 20 f4 7 35.
 4.10.37: Find f.f x 2 12x f 0 9 f 2 15 f
 4.10.38: Find f.f x 20x , , f0 8 f1 5 3 12x 2 4 f x
 4.10.39: Find f.x 2 cos x f 0 1 f 2 0 ; 50.
 4.10.40: Find f.f t 2e f 0 0 f 0 t 3 sin t f
 4.10.41: Find f.f x x x 0 f 1 0 f 2 0 2f
 4.10.42: Find f.f x sin x f 0 1 f 0 1 f 0 1 f
 4.10.43: Given that the graph of passes through the point and that the slope...
 4.10.44: Find a function such that and the line is tangent to the graph of
 4.10.45: The graph of a function is shown. Which graph is an antiderivative ...
 4.10.46: The graph of a function is shown. Which graph is an antiderivative ...
 4.10.47: The graph of a function is shown in the figure. Make a rough sketch...
 4.10.48: The graph of the velocity function of a car is shown in the figure....
 4.10.49: The graph of is shown in the figure. Sketch the graph of if is cont...
 4.10.50: (a) Use a graphing device to graph . (b) Starting with the graph in...
 4.10.51: Draw a graph of and use it to make a rough sketch of the antideriva...
 4.10.52: Draw a graph of and use it to make a rough sketch of the antideriva...
 4.10.53: A direction field is given for a function. Use it to draw the antid...
 4.10.54: A direction field is given for a function. Use it to draw the antid...
 4.10.55: Use a direction field to graph the antiderivative that satisfies .
 4.10.56: Use a direction field to graph the antiderivative that satisfies .
 4.10.57: A function is defined by the following experimental data. Use a dir...
 4.10.58: (a) Draw a direction field for the function and use it to sketch se...
 4.10.59: A particle is moving with the given data. Find the position of the ...
 4.10.60: A particle is moving with the given data. Find the position of the ...
 4.10.61: A particle is moving with the given data. Find the position of the ...
 4.10.62: A particle is moving with the given data. Find the position of the ...
 4.10.63: A particle is moving with the given data. Find the position of the ...
 4.10.64: A particle is moving with the given data. Find the position of the ...
 4.10.65: A stone is dropped from the upper observation deck (the Space Deck)...
 4.10.66: Show that for motion in a straight line with constant acceleration ...
 4.10.67: An object is projected upward with initial velocity meters per seco...
 4.10.68: Two balls are thrown upward from the edge of the cliff in Example 8...
 4.10.69: A stone was dropped off a cliff and hit the ground with a speed of ...
 4.10.70: If a diver of mass stands at the end of a diving board with length ...
 4.10.71: A company estimates that the marginal cost (in dollars per item) of...
 4.10.72: The linear density of a rod of length m is given by , in grams per ...
 4.10.73: Since raindrops grow as they fall, their surface area increases and...
 4.10.74: A car is traveling at 50 mih when the brakes are fully applied, pro...
 4.10.75: What constant acceleration is required to increase the speed of a c...
 4.10.76: A car braked with a constant deceleration of 16 fts , producing ski...
 4.10.77: A car is traveling at when the driver sees an accident 80 m ahead a...
 4.10.78: A model rocket is fired vertically upward from rest. Its accelerati...
 4.10.79: A highspeed bullet train accelerates and decelerates at the rate o...
Solutions for Chapter 4.10: Antiderivatives
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 4.10: Antiderivatives
Get Full SolutionsCalculus, was written by and is associated to the ISBN: 9780534393397. Since 79 problems in chapter 4.10: Antiderivatives have been answered, more than 45029 students have viewed full stepbystep solutions from this chapter. Chapter 4.10: Antiderivatives includes 79 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Base
See Exponential function, Logarithmic function, nth power of a.

Closed interval
An interval that includes its endpoints

Elementary row operations
The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

Elimination method
A method of solving a system of linear equations

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

Focal length of a parabola
The directed distance from the vertex to the focus.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Imaginary part of a complex number
See Complex number.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Nappe
See Right circular cone.

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Sequence
See Finite sequence, Infinite sequence.

Spiral of Archimedes
The graph of the polar curve.

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

Variation
See Power function.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.