Match the following Column-I with Column-II (A) lim x ( x 2 + 2 x - 1 2 x 2 - 3 x - 2 ) 2 x + 1 2 x - 1 = (P) 1 2 (B) lim x 0 log sec ( x / 2 )

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Solution

Q.
Match the following Column-I with Column-II

Column-I Column-II

(A) $\lim_{x \to \infty} {(\frac{x^{2} + 2 x - 1}{2 x^{2} - 3 x - 2})}^{\frac{2 x + 1}{2 x - 1}} =$ (P) $\frac{1}{2}$

(B) $\lim_{x \to 0} \frac{\log_{\sec (x / 2)} \cos x}{\log_{\sec x} \cos \frac{x}{2}} =$ (Q) $2$

(C)
$Let f (x) = \max (\cos x, x, 2 x - 1), where x \geq 0, then$

$number of points of non-differentiability of f (x) is$
(R) $5$

(D)
$If f (x) = [2 + 3 \sin x], 0 < x < π, then number of$

$points at which the function is discontinuous, is$
(S) $16$

1 A-P, B-S, C-Q, D-R

2 A-S, B-Q, C-P, D-R

3 A-P, B-Q, C-S, D-R

4 A-P, B-S, C-R, D-Q

Ans.
(1)

$A)$ $\lim_{x \to \infty} {(\frac{x^{2} + 2 x - 1}{2 x^{2} - 3 x - 2})}^{\frac{2 x + 1}{2 x - 1}} = \frac{1}{2}$

$B)$ $\lim_{x \to 0} \frac{\log_{\sec (x / 2)} \cos x}{\log_{\sec x} \cos \frac{x}{2}} = \lim_{x \to 0} {(\log_{\sec \frac{x}{2}} \cos x)}^{2} = \lim_{x \to 0} {(\frac{lncos x}{lnsec \frac{x}{2}})}^{2} = 2$

$C)$

$D)$ $\sin x \neq \frac{1}{3}, \frac{2}{3}, \frac{3}{3}$

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