﻿ Critical Points and L'hoptial's Rule Worksheet | Problems & Solutions
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# Critical Points and L'hoptial's Rule Worksheet

Critical Points and L'hoptial's Rule Worksheet
• Page 1
1.
Evaluate $\underset{a\to \infty }{\mathrm{lim}}$.
 a. 36 b. 1 c. 9

Correct answer : (1)
2.
Evaluate $\underset{x\to 0}{\mathrm{lim}}$().
 a. - $\frac{1}{2}$ b. 1 c. $\frac{1}{2}$

Correct answer : (4)
3.
Find the critical numbers for the function $f$($t$) = 10 $t$ ${e}^{19-18{t}^{2}}$.
 a. - $\frac{1}{1296}$, $\frac{1}{1296}$ b. - $\frac{1}{6}$, $\frac{1}{6}$ c. - $\frac{1}{36}$, $\frac{1}{36}$ d. (0, 0)

Correct answer : (2)
4.
Find the critical point of the function $f$($x$) = ${e}^{x{e}^{6x}}$.
 a. (- 6, 1) b. (6, 1.06) c. (0, 2.7183) d. (- $\frac{1}{6}$, 0.94)

Correct answer : (4)
5.
Find the critical numbers for the function $f$($x$) = $x$2($x$2 - 8).
 a. - 2, 0, 2 b. - 1.41, 1.41 c. - 2, 2

Correct answer : (1)
6.
Evaluate .
 a. $\frac{1}{2}$ b. $\frac{9}{10}$ c. $\frac{5}{9}$ d. $\frac{9}{5}$

Correct answer : (2)
7.
Evaluate $\underset{a\to 4}{\mathrm{lim}}$ [].
 a. $e$ b. 1 c. - 1

Correct answer : (3)
8.
Evaluate $\underset{x\to \infty }{\mathrm{lim}}$ $\frac{x}{{3}^{x}}$.
 a. 1 b. ln 3 c.

Correct answer : (1)
9.
Evaluate $\underset{c\to 2}{\mathrm{lim}}$.
 a. $e$-2 b. $e$3 c. $e$2

Correct answer : (4)
10.
Evaluate $\underset{a\to 4}{\mathrm{lim}}$.
 a. $\frac{1}{5}$ b. $\frac{3}{4}$ c. 1 d. $\frac{1}{4}$