Differentiation Question 204
Question: If $ \underset{x\to 0}{\mathop{\lim }}{{(1+asinx)}^{\cos ecx}}=3. $ then a is
Options:
A) ln 2
B) ln 3
C) ln 4
D) $ e^{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given $ 3=\underset{x\to 0}{\mathop{\lim }}{{(1+asinx)}^{\cos ecx}}[{1^{\infty }}form] $ Put $ \sin x=4 $
$ \therefore $ when $ x\to 0,y\to 0 $
$ \therefore \underset{x\to 0}{\mathop{Lim}}{{(1+asinx)}^{\cos ecx}}=\underset{y\to 0}{\mathop{Lim}}{{(1+ay)}^{1/y}}=e^{a} $
$ \therefore e^{a}=3\Rightarrow a={\log _{e}}3=ln3. $
BETA
