 4.1.1: In Exercises 1 4, verify the statement by showing that the derivati...
 4.1.2: In Exercises 1 4, verify the statement by showing that the derivati...
 4.1.3: In Exercises 1 4, verify the statement by showing that the derivati...
 4.1.4: In Exercises 1 4, verify the statement by showing that the derivati...
 4.1.5: In Exercises 58, find the general solution of the differential equa...
 4.1.6: In Exercises 58, find the general solution of the differential equa...
 4.1.7: In Exercises 58, find the general solution of the differential equa...
 4.1.8: In Exercises 58, find the general solution of the differential equa...
 4.1.9: In Exercises 914, complete the table. 2y3
 4.1.10: In Exercises 914, complete the table. 2y3
 4.1.11: In Exercises 914, complete the table. y32
 4.1.12: In Exercises 914, complete the table. 32
 4.1.13: In Exercises 914, complete the table. 32
 4.1.14: In Exercises 914, complete the table. 2x
 4.1.15: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.16: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.17: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.18: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.19: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.20: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.21: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.22: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.23: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.24: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.25: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.26: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.27: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.28: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.29: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.30: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.31: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.32: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.33: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.34: In Exercises 1534, find the indefinite integral and check the resul...
 4.1.35: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.36: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.37: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.38: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.39: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.40: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.41: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.42: In Exercises 3542, find the indefinite integral and check the resul...
 4.1.43: In Exercises 4346, the graph of the derivative of a function is giv...
 4.1.44: In Exercises 4346, the graph of the derivative of a function is giv...
 4.1.45: In Exercises 4346, the graph of the derivative of a function is giv...
 4.1.46: In Exercises 4346, the graph of the derivative of a function is giv...
 4.1.47: In Exercises 47 and 48, find the equation for given the derivative ...
 4.1.48: In Exercises 47 and 48, find the equation for given the derivative ...
 4.1.49: Slope Fields In Exercises 4952, a differential equation, a point, a...
 4.1.50: Slope Fields In Exercises 4952, a differential equation, a point, a...
 4.1.51: Slope Fields In Exercises 4952, a differential equation, a point, a...
 4.1.52: Slope Fields In Exercises 4952, a differential equation, a point, a...
 4.1.53: Slope Fields In Exercises 53 and 54, (a) use a graphing utility to ...
 4.1.54: Slope Fields In Exercises 53 and 54, (a) use a graphing utility to ...
 4.1.55: In Exercises 5562, solve the differential equation. x2
 4.1.56: In Exercises 5562, solve the differential equation. x2x
 4.1.57: In Exercises 5562, solve the differential equation. 2x,
 4.1.58: In Exercises 5562, solve the differential equation. 2x,
 4.1.59: In Exercises 5562, solve the differential equation. x, 4
 4.1.60: In Exercises 5562, solve the differential equation. x, 4
 4.1.61: In Exercises 5562, solve the differential equation. , 4
 4.1.62: In Exercises 5562, solve the differential equation. 4
 4.1.63: Tree Growth An evergreen nursery usually sells a certain shrub afte...
 4.1.64: Population Growth The rate of growth of a population of bacteria is...
 4.1.65: Use the graph of shown in the figure to answer the following, given...
 4.1.66: The graphs of and each pass through the origin. Use the graph of sh...
 4.1.67: Vertical Motion In Exercises 6770, use feet per second per second a...
 4.1.68: Vertical Motion In Exercises 6770, use feet per second per second a...
 4.1.69: Vertical Motion In Exercises 6770, use feet per second per second a...
 4.1.70: Vertical Motion In Exercises 6770, use feet per second per second a...
 4.1.71: Vertical Motion In Exercises 7174, use meters per second per second...
 4.1.72: Vertical Motion In Exercises 7174, use meters per second per second...
 4.1.73: Vertical Motion In Exercises 7174, use meters per second per second...
 4.1.74: Vertical Motion In Exercises 7174, use meters per second per second...
 4.1.75: Lunar Gravity On the moon, the acceleration due to gravity is meter...
 4.1.76: Escape Velocity The minimum velocity required for an object to esca...
 4.1.77: Rectilinear Motion In Exercises 7780, consider a particle moving al...
 4.1.78: Rectilinear Motion In Exercises 7780, consider a particle moving al...
 4.1.79: Rectilinear Motion In Exercises 7780, consider a particle moving al...
 4.1.80: Rectilinear Motion In Exercises 7780, consider a particle moving al...
 4.1.81: Acceleration The maker of an automobile advertises that it takes 13...
 4.1.82: Deceleration A car traveling at 45 miles per hour is brought to a s...
 4.1.83: Acceleration At the instant the traffic light turns green, a car th...
 4.1.84: Modeling Data The table shows the velocities (in miles per hour) of...
 4.1.85: Acceleration Assume that a fully loaded plane starting from rest ha...
 4.1.86: Airplane Separation Two airplanes are in a straightline landing pa...
 4.1.87: True or False? In Exercises 8792, determine whether the statement i...
 4.1.88: True or False? In Exercises 8792, determine whether the statement i...
 4.1.89: True or False? In Exercises 8792, determine whether the statement i...
 4.1.90: True or False? In Exercises 8792, determine whether the statement i...
 4.1.91: True or False? In Exercises 8792, determine whether the statement i...
 4.1.92: True or False? In Exercises 8792, determine whether the statement i...
 4.1.93: Find a function such that the graph of has a horizontal tangent at ...
 4.1.94: The graph of is shown. Sketch the graph of given that is continuous...
 4.1.95: If is continuous, and find Is differentiable at x
 4.1.96: Let be two functions satisfying and for all If prove that x10
 4.1.97: Suppose and are nonconstant, differentiable, realvalued functions ...
Solutions for Chapter 4.1: Antiderivatives and Indefinite Integration
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 4.1: Antiderivatives and Indefinite Integration
Get Full SolutionsChapter 4.1: Antiderivatives and Indefinite Integration includes 97 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981. This textbook survival guide was created for the textbook: Calculus, edition: 8. Since 97 problems in chapter 4.1: Antiderivatives and Indefinite Integration have been answered, more than 78360 students have viewed full stepbystep solutions from this chapter.

Amplitude
See Sinusoid.

Axis of symmetry
See Line of symmetry.

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Inductive step
See Mathematical induction.

Local extremum
A local maximum or a local minimum

Logarithm
An expression of the form logb x (see Logarithmic function)

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Parameter
See Parametric equations.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Sum identity
An identity involving a trigonometric function of u + v

Third quartile
See Quartile.

Unit ratio
See Conversion factor.

Xmin
The xvalue of the left side of the viewing window,.