$\lim _{x \rightarrow 0} \frac{a^x-b^x}{e^x-1}$ is equal to
43 views
0 Votes
0 Votes

$\lim _{x \rightarrow 0} \frac{a^x-b^x}{e^x-1}$ is equal to

(A) $\log \left(\frac{a}{b}\right)$

(B) $\log \left(\frac{b}{a}\right)$

(C) $\log (a b)$

(D) $\log (a+b)$

1 Answer

0 Votes
0 Votes
 
Best answer

SOLUTION —

$\lim _{x \rightarrow 0} \frac{a^x-b^x}{e^x-1} =\lim _{x \rightarrow 0} \frac{a^x-b^x}{x} \cdot \frac{x}{e^x-1}$

$=\lim _{x \rightarrow 0}\left[\frac{a^x-1}{x}-\frac{b^x-1}{x}\right] \frac{x}{e^x-1}$

$=\left[\lim _{x \rightarrow 0}\left(\frac{a^x-1}{x}\right)-\lim _{x \rightarrow 0}\left(\frac{b^x-1}{x}\right)\right] \lim _{x \rightarrow 0} \frac{1}{\frac{e^x-1}{x}}$

$=\left(\log _e a-\log _e b\right) \frac{1}{1}$

$ =\log _e\left(\frac{a}{b}\right)$

So, The correct option will be (A).

RELATED DOUBTS

1 Answer
0 Votes
0 Votes
45 Views
1 Answer
0 Votes
0 Votes
50 Views
1 Answer
0 Votes
0 Votes
53 Views
1 Answer
0 Votes
0 Votes
72 Views
1 Answer
0 Votes
0 Votes
48 Views
1 Answer
0 Votes
0 Votes
67 Views
1 Answer
0 Votes
0 Votes
54 Views
1 Answer
0 Votes
0 Votes
58 Views
1 Answer
0 Votes
0 Votes
59 Views
1 Answer
0 Votes
0 Votes
51 Views
1 Answer
0 Votes
0 Votes
55 Views
1 Answer
0 Votes
0 Votes
83 Views
1 Answer
0 Votes
0 Votes
30 Views
Peddia is an Online Question and Answer Website, That Helps You To Prepare India's All States Boards & Competitive Exams Like IIT-JEE, NEET, AIIMS, AIPMT, SSC, BANKING, BSEB, UP Board, RBSE, HPBOSE, MPBSE, CBSE & Other General Exams.
If You Have Any Query/Suggestion Regarding This Website or Post, Please Contact Us On : [email protected]

CATEGORIES