 4.8.1E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.2E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.3E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.4E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.5E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.6E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.7E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.8E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.9E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.10E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.11E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.12E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.13E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.14E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.15E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.16E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.17E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.18E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.19E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.20E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.21E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.22E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.23E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.24E: In Exercises 1–24, find an antiderivative for each function. Do as ...
 4.8.25E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.26E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.27E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.28E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.29E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.30E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.31E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.32E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.33E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.34E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.35E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.36E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.37E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.38E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.39E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.40E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.41E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.42E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.43E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.44E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.45E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.46E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.47E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.48E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.49E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.50E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.51E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.52E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.53E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.54E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.55E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.56E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.57E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.58E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.59E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.60E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.61E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.62E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.63E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.64E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.65E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.66E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.67E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.68E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.69E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.70E: In Exercises 25–70, find the most general antiderivative or indefin...
 4.8.71E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.72E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.73E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.74E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.75E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.76E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.77E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.78E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.79E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.80E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.81E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.82E: Verify the formulas in Exercises 71–82 by differentiation.
 4.8.83E: Right, or wrong? Say which for each formula and give a brief reason...
 4.8.84E: Right, or wrong? Say which for each formula and give a brief reason...
 4.8.85E: Right, or wrong? Say which for each formula and give a brief reason...
 4.8.86E: Right, or wrong? Say which for each formula and give a brief reason...
 4.8.87E: Right, or wrong? Give a brief reason why.
 4.8.88E: Right, or wrong? Give a brief reason why.
 4.8.89E: Which of the following graphs shows the solution of the initial val...
 4.8.90E: Which of the following graphs shows the solution of the initial val...
 4.8.91E: Solve the initial value problems in Exercises 91–112.
 4.8.92E: Solve the initial value problems in Exercises 91–112.
 4.8.93E: Solve the initial value problems in Exercises 91–112.
 4.8.94E: Solve the initial value problems in Exercises 91–112.
 4.8.95E: Solve the initial value problems in Exercises 91–112.
 4.8.96E: Solve the initial value problems in Exercises 91–112.
 4.8.97E: Solve the initial value problems in Exercises 91–112.
 4.8.98E: Solve the initial value problems in Exercises 91–112.
 4.8.99E: Solve the initial value problems in Exercises 91–112.
 4.8.100E: Solve the initial value problems in Exercises 91–112.
 4.8.101E: Solve the initial value problems in Exercises 91–112.
 4.8.102E: Solve the initial value problems in Exercises 91–112.
 4.8.103E: Solve the initial value problems in Exercises 91–112.
 4.8.104E: Solve the initial value problems in Exercises 91–112.
 4.8.105E: Solve the initial value problems in Exercises 91–112.
 4.8.106E: Solve the initial value problems in Exercises 91–112.
 4.8.107E: Solve the initial value problems in Exercises 91–112.
 4.8.108E: Solve the initial value problems in Exercises 91–112.
 4.8.109E: Solve the initial value problems in Exercises 91–112.
 4.8.110E: Solve the initial value problems in Exercises 91–112.
 4.8.111E: Solve the initial value problems in Exercises 91–112.
 4.8.112E: Solve the initial value problems in Exercises 91–112.
 4.8.113E: Find the curve y = ƒ(x) in the xyplane that passes through the poi...
 4.8.114E: a. Find a curve y = ƒ(x) with the following properties: ii) Its gra...
 4.8.115E: Exercises 115–118 show solution curves of differential equations. I...
 4.8.116E: Exercises 115–118 show solution curves of differential equations. I...
 4.8.117E: Exercises 115–118 show solution curves of differential equations. I...
 4.8.118E: Exercises 115–118 show solution curves of differential equations. I...
 4.8.119E: Finding displacement from an antiderivative of velocitya. Suppose t...
 4.8.120E: Liftoff from Earth A rocket lifts off the surface of Earth with a c...
 4.8.121E: Stopping a car in time You are driving along a highway at a steady ...
 4.8.122E: Stopping a motorcycle The State of Illinois Cycle Rider Safety Prog...
 4.8.123E: Motion along a coordinate line A particle moves on a coordinate lin...
 4.8.124E: The hammer and the feather When Apollo 15 astronaut David Scott dro...
 4.8.125E: Motion with constant acceleration The standard equation for the pos...
 4.8.126E: Free fall near the surface of a planet For free fall near the surfa...
 4.8.127E: Suppose that Find:
 4.8.128E: Uniqueness of solutions If differentiable functions y = F(x) and y ...
 4.8.129CE: Use a CAS to solve the initial value problems in Exercises 129–132....
 4.8.130CE: Use a CAS to solve the initial value problems in Exercises 129–132....
 4.8.131CE: Use a CAS to solve the initial value problems in Exercises 129–132....
 4.8.132CE: Use a CAS to solve the initial value problems in Exercises 129–132....
Solutions for Chapter 4.8: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 4.8
Get Full SolutionsThis textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Since 132 problems in chapter 4.8 have been answered, more than 61639 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. Chapter 4.8 includes 132 full stepbystep solutions.

Absolute value of a vector
See Magnitude of a vector.

Amplitude
See Sinusoid.

Arcsine function
See Inverse sine function.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Cubic
A degree 3 polynomial function

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Equation
A statement of equality between two expressions.

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Leading coefficient
See Polynomial function in x

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

nset
A set of n objects.

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Positive angle
Angle generated by a counterclockwise rotation.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Yscl
The scale of the tick marks on the yaxis in a viewing window.