 5.3.87E: We say ƒ is uniformly continuous on [a, b] if given any there is a ...
 5.3.1E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.2E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.3E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.4E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.5E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.6E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.7E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.8E: Express the limits in Exercises 1–8 as definite integrals. where P ...
 5.3.9E: Suppose that ƒ and g are integrable and that Use the rules in Table...
 5.3.10E: Suppose that ƒ and h are integrable and that Use the rules in Table...
 5.3.11E: Suppose that Find
 5.3.12E: Suppose that Find
 5.3.13E: Suppose that ƒ is integrable and that and Find
 5.3.14E: Suppose that h is integrable and that and Find
 5.3.15E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.16E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.17E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.18E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.19E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.20E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.21E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.22E: In Exercises 15–22, graph the integrands and use areas to evaluate ...
 5.3.23E: Use areas to evaluate the integrals in Exercises 23–28.
 5.3.24E: Use areas to evaluate the integrals in Exercises 23–28.
 5.3.25E: Use areas to evaluate the integrals in Exercises 23–28.
 5.3.26E: Use areas to evaluate the integrals in Exercises 23–28.
 5.3.27E: Use areas to evaluate the integrals in Exercises 23–28. on a. [2, ...
 5.3.28E: Use areas to evaluate the integrals in Exercises 23–28. on a. [1, ...
 5.3.29E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.30E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.31E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.32E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.33E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.34E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.35E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.36E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.37E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.38E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.39E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.40E: Use the results of Equations (2) and (4) to evaluate the integrals ...
 5.3.41E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.42E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.43E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.44E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.45E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.46E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.47E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.48E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.49E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.50E: Use the rules in Table 5.4 and Equations (2)–(4) to evaluate the in...
 5.3.51E: In Exercises 51–54, use a definite integral to find the area of the...
 5.3.52E: In Exercises 51–54, use a definite integral to find the area of the...
 5.3.53E: In Exercises 51–54, use a definite integral to find the area of the...
 5.3.54E: In Exercises 51–54, use a definite integral to find the area of the...
 5.3.55E: In Exercises 55–62, graph the function and find its average value o...
 5.3.56E: In Exercises 55–62, graph the function and find its average value o...
 5.3.57E: In Exercises 55–62, graph the function and find its average value o...
 5.3.58E: In Exercises 55–62, graph the function and find its average value o...
 5.3.59E: In Exercises 55–62, graph the function and find its average value o...
 5.3.60E: In Exercises 55–62, graph the function and find its average value o...
 5.3.61E: In Exercises 55–62, graph the function and find its average value o...
 5.3.62E: In Exercises 55–62, graph the function and find its average value o...
 5.3.63E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.64E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.65E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.66E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.67E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.68E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.69E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.70E: Use the method of Example 4a or Equation (1) to evaluate the defini...
 5.3.71E: What values of a and b maximize the value of (Hint: Where is the in...
 5.3.72E: What values of a and b minimize the value of
 5.3.73E: Use the MaxMin Inequality to find upper and lower bounds for the v...
 5.3.74E: (Continuation of Exercise 73.) Use the MaxMin Inequality to find u...
 5.3.75E: Show that the value of cannot possibly be 2.
 5.3.76E: Show that the value of lies between and 3.
 5.3.77E: Integrals of nonnegative functions Use the MaxMin Inequality to sh...
 5.3.78E: Integrals of nonpositive functions Show that if ƒ is integrable then
 5.3.79E: Use the inequality sin x ? x, which holds for x ? 0, to find an upp...
 5.3.80E: The inequality sec x ? 1 + (x2/2) holds on (?/2, ?/2). Use it to f...
 5.3.81E: If av(ƒ) really is a typical value of the integrable function ƒ(x) ...
 5.3.82E: It would be nice if average values of integrable functions obeyed t...
 5.3.83E: Upper and lower sums for increasing functionsa. Suppose the graph o...
 5.3.84E: Upper and lower sums for decreasing functions (Continuation of Exer...
 5.3.85E: Use the formula to find the area under the curve y = sin x from x =...
 5.3.86E: Suppose that ƒ is continuous and nonnegative over [a, b], as in the...
 5.3.88E: If you average 30 mi/h on a 150mi trip and then return over the sa...
 5.3.89CE: If your CAS can draw rectangles associated with Riemann sums, use i...
 5.3.90CE: If your CAS can draw rectangles associated with Riemann sums, use i...
 5.3.91CE: If your CAS can draw rectangles associated with Riemann sums, use i...
 5.3.92CE: If your CAS can draw rectangles associated with Riemann sums, use i...
 5.3.93CE: If your CAS can draw rectangles associated with Riemann sums, use i...
 5.3.94CE: If your CAS can draw rectangles associated with Riemann sums, use i...
 5.3.95CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.96CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.97CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.98CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.99CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.100CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.101CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
 5.3.102CE: In Exercises 95–102, use a CAS to perform the following steps:a. Pl...
Solutions for Chapter 5.3: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 5.3
Get Full SolutionsThis textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Since 102 problems in chapter 5.3 have been answered, more than 61027 students have viewed full stepbystep solutions from this chapter. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.3 includes 102 full stepbystep solutions.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

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.

Cone
See Right circular cone.

Confounding variable
A third variable that affects either of two variables being studied, making inferences about causation unreliable

Continuous function
A function that is continuous on its entire domain

Cubic
A degree 3 polynomial function

Equivalent systems of equations
Systems of equations that have the same solution.

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Frequency table (in statistics)
A table showing frequencies.

Imaginary unit
The complex number.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Order of magnitude (of n)
log n.

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Outcomes
The various possible results of an experiment.

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

Positive numbers
Real numbers shown to the right of the origin on a number line.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Resistant measure
A statistical measure that does not change much in response to outliers.

Vertex of an angle
See Angle.