displaystyle limx → 1 ( tan (x2-1)/x-1) is equal to

Question

displaystyle limx → 1 ( tan (x2-1)/x-1) is equal to (A)  (1/2) (B) 2 (C)  (-1/2) (D) -2

Tardigrade Admin · Accepted Answer

We have, displaystyle limx→1 ( tan(x2-1)/x-1) ((0/0) text form ) = displaystyle limx→1 ( sec2 (x2 -1) .2x/1) [using Lâ Hospitalâs rule] = 2. sec2 (0) = 2

Q. $x \to 1 lim \frac{tan ( x ^{2} - 1 )}{x - 1}$ is equal to

$\frac{1}{2}$

$2$

$\frac{- 1}{2}$

$- 2$

We have, $x \to 1 lim \frac{tan ( x ^{2} - 1 )}{x - 1}$ $(\frac{0}{0} form)$
$= x \to 1 lim \frac{sec ^{2} ( x ^{2} - 1 ) .2 x}{1}$
[using L’ Hospital’s rule]
$= 2. sec^{2} (0) = 2$

Q. x→1lim​x−1tan(x2−1)​ is equal to

21​

2

2−1​

−2

We have, x→1lim​x−1tan(x2−1)​ (00​ form ) =x→1lim​1sec2(x2−1).2x​ [using L’ Hospital’s rule] =2.sec2(0)=2

Q. $x \to 1 lim \frac{tan ( x ^{2} - 1 )}{x - 1}$ is equal to

$\frac{1}{2}$

$2$

$\frac{- 1}{2}$

$- 2$

We have, $x \to 1 lim \frac{tan ( x ^{2} - 1 )}{x - 1}$ $(\frac{0}{0} form)$
$= x \to 1 lim \frac{sec ^{2} ( x ^{2} - 1 ) .2 x}{1}$
[using L’ Hospital’s rule]
$= 2. sec^{2} (0) = 2$