 1.6.1: 1. In each part, is the given function continuous on the interval[0...
 1.6.2: Evaluate(a) limx0sin xx(b) limx01 cos xx
 1.6.3: Suppose a function f has the property that for all real numbersx 3 ...
 1.6.4: In each part, give the largest interval on which the functionis con...
 1.6.5: 18 Find the discontinuities, if any. f(x) = csc x
 1.6.6: 18 Find the discontinuities, if any. f(x) = 11 + sin2 x
 1.6.7: 18 Find the discontinuities, if any. f(x) = 11 2 sin x
 1.6.8: 18 Find the discontinuities, if any. f(x) =2 + tan2 x
 1.6.9: 914 Determine where f is continuous. f(x) = sin1 2x
 1.6.10: 914 Determine where f is continuous. f(x) = cos1(ln x)
 1.6.11: 914 Determine where f is continuous. f(x) = ln(tan1 x)x2 9
 1.6.12: 914 Determine where f is continuous. f(x) = expsin xx
 1.6.13: 914 Determine where f is continuous. f(x) = sin1(1/x)x
 1.6.14: 914 Determine where f is continuous. f(x) = ln x 2 ln(x+3)
 1.6.15: 1516 In each part, use Theorem 1.5.6(b) to show that the function i...
 1.6.16: 1516 In each part, use Theorem 1.5.6(b) to show that the function i...
 1.6.17: 1740 Find the limits. limx+cos1x
 1.6.18: 1740 Find the limits. x+sin x2 3x
 1.6.19: 1740 Find the limits. limx+sin1 x1 2x
 1.6.20: 1740 Find the limits. imx+ln x + 1x
 1.6.21: 1740 Find the limits. limx0esin x
 1.6.22: 1740 Find the limits. limx+cos(2 tan1 x)
 1.6.23: 1740 Find the limits. lim 0sin 3
 1.6.24: 1740 Find the limits. limh0sin h2h
 1.6.25: 1740 Find the limits. lim 0+sin 2
 1.6.26: 1740 Find the limits. lim 0sin2
 1.6.27: 1740 Find the limits. limx0tan 7xsin 3x
 1.6.28: 1740 Find the limits. limx0sin 6xsin 8x
 1.6.29: 1740 Find the limits. limx0+sin x5x
 1.6.30: 1740 Find the limits. limx0sin2 x3x2
 1.6.31: 1740 Find the limits. limx0sin x2x
 1.6.32: 1740 Find the limits. limh0sin h1 cos h
 1.6.33: 1740 Find the limits. . limt 0t 21 cos2 t
 1.6.34: 1740 Find the limits. limx0xcos 12 x
 1.6.35: 1740 Find the limits. lim 0 21 cos
 1.6.36: 1740 Find the limits. limh01 cos 3hcos2 5h 1
 1.6.37: 1740 Find the limits. limx0+ sin 1x
 1.6.38: 1740 Find the limits. imx0x2 3 sin xx
 1.6.39: 1740 Find the limits. limx02 cos 3x cos 4xx
 1.6.40: 1740 Find the limits. limx0tan 3x2 + sin2 5xx2
 1.6.41: 4142 (a) Complete the table and make a guess about the limit indica...
 1.6.42: 4142 (a) Complete the table and make a guess about the limit indica...
 1.6.43: 4346 TrueFalse Determine whether the statement is true or false. Ex...
 1.6.44: 4346 TrueFalse Determine whether the statement is true or false. Ex...
 1.6.45: 4346 TrueFalse Determine whether the statement is true or false. Ex...
 1.6.46: 4346 TrueFalse Determine whether the statement is true or false. Ex...
 1.6.47: In an attempt to verify that limx0 (sin x)/x = 1, a studentconstruc...
 1.6.48: In the circle in the accompanying figure, a central angleof measure...
 1.6.49: Find a nonzero value for the constant k that makesf(x) =tan kxx , x...
 1.6.50: Isf(x) =sin xx , x = 01, x = 0continuous at x = 0? Explain.
 1.6.51: In parts (a)(c), find the limit by making the indicated substitutio...
 1.6.52: Find limx2cos(/x)x 2 .Hint: Let t = 2 x.
 1.6.53: Find limx1sin(x)x 1 .
 1.6.54: Find lim x/4tan x1x/4
 1.6.55: Find lim x/4cos x sin xx /4
 1.6.56: Suppose that f is an invertible function, f (0) = 0, f iscontinuous...
 1.6.57: 5760 Apply the result of Exercise 56, if needed, to find the limits...
 1.6.58: 5760 Apply the result of Exercise 56, if needed, to find the limits...
 1.6.59: 5760 Apply the result of Exercise 56, if needed, to find the limits...
 1.6.60: 5760 Apply the result of Exercise 56, if needed, to find the limits...
 1.6.61: Use the Squeezing Theorem to show thatlimx0x cos 50x = 0and illustr...
 1.6.62: Use the Squeezing Theorem to show thatlimx0x2 sin 50 3 x= 0and illu...
 1.6.63: . In Example 5 we used the Squeezing Theorem to provethatlimx0x sin...
 1.6.64: Sketch the graphs of the curves y = 1 x2, y = cos x,and y = f(x), w...
 1.6.65: Sketch the graphs of the curves y = 1/x, y = 1/x,and y = f(x), wher...
 1.6.66: Draw pictures analogous to Figure 1.6.2 that illustratethe Squeezin...
 1.6.67: (a) Use the IntermediateValue Theorem to show that theequation x =...
 1.6.68: (a) Use the IntermediateValue Theorem to show that theequation x +...
 1.6.69: In the study of falling objects near the surface of the Earth,the a...
 1.6.70: Writing In your own words, explain the practical value ofthe Squeez...
 1.6.71: Writing A careful examination of the proof of Theorem1.6.5 raises t...
Solutions for Chapter 1.6: CONTINUITY OF TRIGONOMETRIC, EXPONENTIAL, AND INVERSE FUNCTIONS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 1.6: CONTINUITY OF TRIGONOMETRIC, EXPONENTIAL, AND INVERSE FUNCTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Chapter 1.6: CONTINUITY OF TRIGONOMETRIC, EXPONENTIAL, AND INVERSE FUNCTIONS includes 71 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 71 problems in chapter 1.6: CONTINUITY OF TRIGONOMETRIC, EXPONENTIAL, AND INVERSE FUNCTIONS have been answered, more than 41663 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691.

Addition property of equality
If u = v and w = z , then u + w = v + z

Arcsine function
See Inverse sine function.

Closed interval
An interval that includes its endpoints

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

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Direction of an arrow
The angle the arrow makes with the positive xaxis

Event
A subset of a sample space.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Limit to growth
See Logistic growth function.

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

Objective function
See Linear programming problem.

Parametric equations
Equations of the form x = ƒ(t) and y = g(t) for all t in an interval I. The variable t is the parameter and I is the parameter interval.

Real number
Any number that can be written as a decimal.

Righthand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Viewing window
The rectangular portion of the coordinate plane specified by the dimensions [Xmin, Xmax] by [Ymin, Ymax].