 6.1: The graph of f is shown. Is f onetoone? Explain.
 6.2: The graph of is given. (a) Why is onetoone? (b) Estimate the valu...
 6.3: Suppose f is onetoone, , and . Find (a) and (b)
 6.4: Find the inverse function of f x x 12x 1y
 6.5: Sketch a rough graph of the function without using a calculator.
 6.6: Sketch a rough graph of the function without using a calculator.
 6.7: Sketch a rough graph of the function without using a calculator.
 6.8: Sketch a rough graph of the function without using a calculator.
 6.9: Sketch a rough graph of the function without using a calculator.
 6.10: Let . For large values of , which of the functions , , and has the ...
 6.11: Find the exact value of each expression.
 6.12: Find the exact value of each expression.
 6.13: Solve the equation for .
 6.14: Solve the equation for .
 6.15: Solve the equation for .
 6.16: Solve the equation for .
 6.17: Solve the equation for .
 6.18: Solve the equation for .
 6.19: Solve the equation for .
 6.20: Solve the equation for .
 6.21: Differentiate.
 6.22: Differentiate.
 6.23: Differentiate.
 6.24: Differentiate.
 6.25: Differentiate.
 6.26: Differentiate.
 6.27: Differentiate.
 6.28: Differentiate.
 6.29: Differentiate.
 6.30: Differentiate.
 6.31: Differentiate.
 6.32: Differentiate.
 6.33: Differentiate.
 6.34: Differentiate.
 6.35: Differentiate.
 6.36: Differentiate.
 6.37: Differentiate.
 6.38: Differentiate.
 6.39: Differentiate.
 6.40: Differentiate.
 6.41: Differentiate.
 6.42: Differentiate.
 6.43: Differentiate.
 6.44: Differentiate.
 6.45: Differentiate.
 6.46: Differentiate.
 6.47: Differentiate.
 6.48: Show that ddx 12 tan1x 14 ln x 12x 2 1 11 x1 x 2f tf x
 6.49: Find in terms of
 6.50: Find in terms of
 6.51: Find in terms of
 6.52: Find in terms of
 6.55: Use mathematical induction to show that if , then .
 6.56: Find y y x arctan yy
 6.57: Find an equation of the tangent to the curve at the given point.
 6.58: Find an equation of the tangent to the curve at the given point.
 6.59: At what point on the curve is the tangent horizontal?
 6.60: If , find . Graph and on the same screen and comment.
 6.61: (a) Find an equation of the tangent to the curve that is parallel t...
 6.62: The function , where a, b, and K are positive constants and , is us...
 6.63: Evaluate the limit.
 6.64: Evaluate the limit.
 6.65: Evaluate the limit.
 6.66: Evaluate the limit.
 6.67: Evaluate the limit.
 6.68: Evaluate the limit.
 6.69: Evaluate the limit.
 6.70: Evaluate the limit.
 6.71: Evaluate the limit.
 6.72: Evaluate the limit.
 6.73: Evaluate the limit.
 6.74: Evaluate the limit.
 6.75: Evaluate the limit.
 6.76: Evaluate the limit.
 6.77: Evaluate the limit.
 6.78: Evaluate the limit.
 6.79: Sketch the curve using the guidelines of Section 3.5.
 6.80: Sketch the curve using the guidelines of Section 3.5.
 6.81: Sketch the curve using the guidelines of Section 3.5.
 6.82: Sketch the curve using the guidelines of Section 3.5.
 6.83: Sketch the curve using the guidelines of Section 3.5.
 6.84: Sketch the curve using the guidelines of Section 3.5.
 6.85: Investigate the family of curves given by , where is a real number....
 6.86: Investigate the family of functions . What happens to the maximum a...
 6.87: An equation of motion of the form represents damped oscillation of ...
 6.88: (a) Show that there is exactly one root of the equation and that it...
 6.89: A bacteria culture contains 200 cells initially and grows at a rate...
 6.90: Cobalt60 has a halflife of 5.24 years. (a) Find the mass that rem...
 6.91: The biologist G. F. Gause conducted an experiment in the 1930s with...
 6.92: Evaluate the integral.
 6.93: Evaluate the integral.
 6.94: Evaluate the integral.
 6.95: Evaluate the integral.
 6.96: Evaluate the integral.
 6.97: Evaluate the integral.
 6.98: Evaluate the integral.
 6.99: Evaluate the integral.
 6.100: Evaluate the integral.
 6.101: Evaluate the integral.
 6.102: Evaluate the integral.
 6.103: Evaluate the integral.
 6.104: Evaluate the integral.
 6.105: Evaluate the integral.
 6.106: Use properties of integrals to prove the inequality
 6.107: Use properties of integrals to prove the inequality
 6.108: Use properties of integrals to prove the inequality
 6.111: Find the average value of the function on the interval .
 6.112: Find the area of the region bounded by the curves , and .
 6.113: Find the volume of the solid obtained by rotating about the axis t...
 6.114: If , find .
 6.115: If , find .
 6.116: What is the area of the largest rectangle in the first quadrant wit...
 6.117: What is the area of the largest triangle in the first quadrant with...
 6.118: Evaluate without using the Fundamental Theorem of Calculus. [Hint: ...
 6.119: If , where , then, by the Fundamental Theorem, Use lHospitals Rule ...
 6.120: Show that cos arctansinarccot x x 2 1 x 2 2 F1
 6.121: The figure shows two regions in the first quadrant: is the area und...
Solutions for Chapter 6: Calculus, 7th Edition
Full solutions for Calculus,  7th Edition
ISBN: 9780538497817
Solutions for Chapter 6
Get Full SolutionsSince 117 problems in chapter 6 have been answered, more than 7348 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 7. Chapter 6 includes 117 full stepbystep solutions. Calculus, was written by and is associated to the ISBN: 9780538497817.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Course
See Bearing.

Descriptive statistics
The gathering and processing of numerical information

Horizontal component
See Component form of a vector.

Identity
An equation that is always true throughout its domain.

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Logarithmic form
An equation written with logarithms instead of exponents

Modulus
See Absolute value of a complex number.

Octants
The eight regions of space determined by the coordinate planes.

Period
See Periodic function.

Polar equation
An equation in r and ?.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Quartic regression
A procedure for fitting a quartic function to a set of data.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Series
A finite or infinite sum of terms.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Vertical line test
A test for determining whether a graph is a function.