 4.5.1E: In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then ...
 4.5.2E: In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then ...
 4.5.3E: In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then ...
 4.5.4E: In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then ...
 4.5.5E: In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then ...
 4.5.6E: In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then ...
 4.5.7E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.8E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.9E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.10E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.11E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.12E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.13E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.14E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.15E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.16E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.17E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.18E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.19E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.20E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.21E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.22E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.23E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.24E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.25E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.26E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.27E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.28E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.29E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.30E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.31E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.32E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.33E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.34E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.35E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.36E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.37E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.38E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.39E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.40E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.41E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.42E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.43E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.44E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.45E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.46E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.47E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.48E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.49E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.50E: Use l’Hôpital’s rule to find the limits in Exercises 7–50.
 4.5.51E: Find the limits in Exercise 51–66.
 4.5.52E: Find the limits in Exercise 51–66.
 4.5.53E: Find the limits in Exercise 51–66.
 4.5.54E: Find the limits in Exercise 51–66.
 4.5.55E: Find the limits in Exercise 51–66.
 4.5.56E: Find the limits in Exercise 51–66.
 4.5.57E: Find the limits in Exercise 51–66.
 4.5.58E: Find the limits in Exercise 51–66.
 4.5.59E: Find the limits in Exercise 51–66.
 4.5.60E: Find the limits in Exercise 51–66.
 4.5.61E: Find the limits in Exercise 51–66.
 4.5.62E: Find the limits in Exercise 51–66.
 4.5.63E: Find the limits in Exercise 51–66.
 4.5.64E: Find the limits in Exercise 51–66.
 4.5.65E: Find the limits in Exercise 51–66.
 4.5.66E: Find the limits in Exercise 51–66.
 4.5.67E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.68E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.69E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.70E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.71E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.72E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.73E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.74E: L’Hôpital’s Rule does not help with the limits in Exercises 67–74. ...
 4.5.75E: Which one is correct, and which one is wrong? Give reasons for your...
 4.5.76E: Which one is correct, and which one is wrong? Give reasons for your...
 4.5.77E: Only one of these calculations is correct. Which one? Why are the o...
 4.5.78E: Find all values of c that satisfy the conclusion of Cauchy’s Mean V...
 4.5.79E: Continuous extension Find a value of c that makes the function cont...
 4.5.80E: For what values of a and b is
 4.5.81E: ?  ? Forma. Estimate the value of by graphing over a suitably larg...
 4.5.82E: Find
 4.5.84E: This exercise explores the difference between the limit and the lim...
 4.5.85E: Show that
 4.5.86E: Given that x > 0, find the maximum value, if any, of
 4.5.87E: Use limits to find horizontal asymptotes for each function.
 4.5.88E: Find f’(0) for
 4.5.89E: The continuous extension of (sin x)x to [0, ?]a. Graph f(x) =(sin x...
 4.5.90E: The function (sin x)tan x (Continuation of Exercise 89.)a. Graph f(...
Solutions for Chapter 4.5: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 4.5
Get Full SolutionsChapter 4.5 includes 89 full stepbystep solutions. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Since 89 problems in chapter 4.5 have been answered, more than 58364 students have viewed full stepbystep solutions from this chapter. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Arcsecant function
See Inverse secant function.

Commutative properties
a + b = b + a ab = ba

Cosine
The function y = cos x

Direction vector for a line
A vector in the direction of a line in threedimensional space

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Irrational numbers
Real numbers that are not rational, p. 2.

Local extremum
A local maximum or a local minimum

Positive angle
Angle generated by a counterclockwise rotation.

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

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

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Weights
See Weighted mean.