Limits of the type0/, /0, 0, , + + (+),+ (), + (), (+)are not indeterminate forms. Find

Chapter 3, Problem 57

(choose chapter or problem)

Limits of the type

\(0 / \infty, \infty / 0,0^{\infty}, \infty \cdot \infty,+\infty+(+\infty),+\infty-(-\infty),-\infty+(-\infty),-\infty-(+\infty)\)

are not indeterminate forms. Find the following limits by inspection.

(a) \(\lim _{x \rightarrow 0^{+}} \frac{x}{\ln x}\)

(b) \(\lim _{x \rightarrow+\infty} \frac{x^{3}}{e^{-x}}\)

(c) \(\lim _{x \rightarrow(\pi / 2)^{-}}(\cos x)^{\tan x}\)

(d) \(\lim _{x \rightarrow 0^{+}}(\ln x) \cot x\)

(e) \(\lim _{x \rightarrow 0^{+}}\left(\frac{1}{x}-\ln x\right)\)

(f) \(\lim _{x \rightarrow-\infty}\left(x+x^{3}\right)\)

Equation Transcription

Text Transcription:

0/infinity, infinity/0, 0^infinity ,infinity . infinity, +infinity+(+infinity), +infinity-(-infinity), -infinity+(-infinity), -infinity-(+infinity)

lim _x right arrow 0^+ x/ln x

lim _x right arrow + infinity x^3 /e^-x

lim _x right arrow (pi/2)^- (cos x)^tan x

lim _x right arrow 0^+ (lnx)cotx

lim _x right arrow 0^+ (1/x -lnx)

lim _x right arrow - infinity (x+x^3)