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Question

Mathematics Question on Limits and derivations

Match List-I and List-II

LIST I**LIST II **
A.limx0(1+sinx)2cotx\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}
B.limx0ex(1+x)/x2\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2
C.limx0(sinxx)1/x2\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}
D.limx(x+2x+1)x+3\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}

Choose the correct answer from the options given below:

A

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

B

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

C

(A)-(1), (B)-(II), (C)-(III), (D)-(IV)

D

(A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Answer

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Explanation

Solution

The correct answer is(B): (A)-(III), (B)-(IV), (C)-(I), (D)-(II)