Question #320184

Evaluate limits involving the expressions (sin t/t), (1 - cos t)/t) and ((e ^ t- 1)/t) and indeterminate forms type "0/0"



Directions: Create example of limits of functions and evaluate their limits.


1.(sint)/t


2.(1 - cos t)/t


3.(e ^ t - 1)/t




1
Expert's answer
2022-04-01T02:30:27-0400

Using L'Hospital's rule we can write:

limt0sintt=limt0(sint)t=limt0cost1=1\displaystyle\lim_{\mathclap{t\to0}} {\frac{\sin t}{t}}= \lim_{\mathclap{t\to0}}{\frac{(\sin t)’}{t’}}= \lim_{\mathclap{t\to0}} {\frac{\cos t}{1}}=1

limt01costt=limt0(1cost)t=limt0sint1=0\displaystyle\lim_{\mathclap{t\to0}} {\frac{1-\cos t}{t}}= \lim_{\mathclap{t\to0}}{\frac{(1-\cos t)’}{t’}}= \lim_{\mathclap{t\to0}} {\frac{\sin t}{1}}=0

limt0et1t=limt0(et1)t=limt0et1=1\displaystyle\lim_{\mathclap{t\to0}} {\frac{e^t-1}{t}}= \lim_{\mathclap{t\to0}}{\frac{(e^t-1)’}{t’}}= \lim_{\mathclap{t\to0}} {\frac{e^t}{1}}=1


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS