 6.1: The graph of is shown. Is 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) . g y 0 1 x 1 t1 f 7
 6.4: Find the inverse function of
 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.
 6.49: 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
 6.57: 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...
 6.116: 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,
 6.120: Show that cos arctansinarccot x x 2 1 x 2 2 F1
 6.121: If is a continuous function such that for all , find an explicit fo...
 6.122: The figure shows two regions in the first quadrant: is the area und...
Solutions for Chapter 6: Single Variable Calculus 7th Edition
Full solutions for Single Variable Calculus  7th Edition
ISBN: 9780538497831
Solutions for Chapter 6
Get Full SolutionsChapter 6 includes 114 full stepbystep solutions. Since 114 problems in chapter 6 have been answered, more than 5465 students have viewed full stepbystep solutions from this chapter. Single Variable Calculus was written by and is associated to the ISBN: 9780538497831. This textbook survival guide was created for the textbook: Single Variable Calculus, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Gaussian curve
See Normal curve.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Horizontal shrink or stretch
See Shrink, stretch.

Inequality
A statement that compares two quantities using an inequality symbol

Interval
Connected subset of the real number line with at least two points, p. 4.

Interval notation
Notation used to specify intervals, pp. 4, 5.

Length of an arrow
See Magnitude of an arrow.

nth root of unity
A complex number v such that vn = 1

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

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

Perihelion
The closest point to the Sun in a planet’s orbit.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Present value of an annuity T
he net amount of your money put into an annuity.

Slope
Ratio change in y/change in x

Statistic
A number that measures a quantitative variable for a sample from a population.

Unbounded interval
An interval that extends to ? or ? (or both).

yintercept
A point that lies on both the graph and the yaxis.