PROBLEM 01

(1 point)

Given that limxaf(x)=0, limxag(x)=0, limxah(x)=1, limxap(x)=, limxaq(x)=lim�→��(�)=0, lim�→��(�)=0, lim�→�ℎ(�)=1, lim�→��(�)=∞, lim�→��(�)=∞.

Which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible. Enter I to indicate an indeterminate form, INF for positive infinity, NINF for negative infinity, and D for the limit does not exist or we don't have enough information to determine the limit.

(a) limxa[f(x)]g(x)=lim�→�[�(�)]�(�)= 

(b) limxa[f(x)]p(x)=lim�→�[�(�)]�(�)= 

(c) limxa[h(x)]p(x)=lim�→�[ℎ(�)]�(�)= 

(d) limxa[p(x)]f(x)=lim�→�[�(�)]�(�)= 

(e) limxa[p(x)]q(x)=lim�→�[�(�)]�(�)= 

(f) limxap(x)q(x)=lim�→��(�)�(�)= 

台大WEBWORK 微積分1:11~14組 【4.4: Pr

台大WEBWORK 微積分1:11~14組 【4.4: Pr

 

PROBLEM 02

 

4.4: Problem 2

 
 
 
 
 
 
 
 
 

(1 point)

Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D for the limit does not exist.

limx03arcsinx6x=lim�→0−3arcsin⁡�6�= 

You have attempted this problem 1 time.
Your overall recorded score is 100%.
You have unlimited attempts remaining.

台大WEBWORK 微積分1:11~14組 【4.4: Pr

台大WEBWORK 微積分1:11~14組 【4.4: Pr

PROBLEM 03

(1 point)

Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D for the limit does not exist.

limx15lnx5x1=lim�→15ln⁡�−5�−1= 

You have attempted this problem 1 time.
Your overall recorded score is 100%.
You have unlimited attempts remaining.

台大WEBWORK 微積分1:11~14組 【4.4: Pr

台大WEBWORK 微積分1:11~14組 【4.4: Pr

 

PROBLEM 04

1 point)
Evaluate the limit using L'Hospital's rule if necessary.

limx0+x5sin(x)lim�→0+�5sin(�)

Answer: 

 

You have attempted this problem 2 times.
Your overall recorded score is 100%.
You have unlimited attempts remaining.

台大WEBWORK 微積分1:11~14組 【4.4: Pr

台大WEBWORK 微積分1:11~14組 【4.4: Pr

PROBLEM 05

(1 point)
Evaluate the limit using L'Hospital's rule if necessary

limx(1+3x)x11lim�→∞(1+3�)�11

 

You have attempted this problem 1 time.
Your overall recorded score is 100%.
You have unlimited attempts remaining.

台大WEBWORK 微積分1:11~14組 【4.4: Pr

台大WEBWORK 微積分1:11~14組 【4.4: Pr

PROBLEM 06

(1 point) Find the following limits, using l'Hopital's rule if appropriate
limxarctan(x7)x4lim�→∞arctan⁡(�7)�4 = 

limx0+x4ln(x)lim�→0+�4ln⁡(�) = 

Note: You can earn partial credit on this problem.

You have attempted this problem 2 times.
Your overall recorded score is 100%.
You have unlimited attempts remaining.

台大WEBWORK 微積分1:11~14組 【4.4: Pr

台大WEBWORK 微積分1:11~14組 【4.4: Pr

PROBLEM 07

(1 point) Compute

limx0(cosx)1/x2=lim�⟶0(cos⁡�)1/�2= 

You have attempted this problem 1 time.
Your overall recorded score is 100%.
You have unlimited attempts remaining.

台大WEBWORK 微積分1:11~14組 【4.4: Pr

 

 

 

 

 

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