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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Limits

NTA Abhyas 2020 · Mathematics · Limits

If f (x) = \ cases g(x) – 1 x – 1 ; & x ≠ 1 1; & x = 1 cases ) and...

If

f

\left(x\right) = \left\{

\begin{cases}\dfrac{\sqrt{g\left(x\right)} – 1}{\sqrt{x} – 1}; & x \ne 1 \\ 1; & x = 1\end{cases}

\right)

and g^{'} \left(1\right) = 2, g \left(1\right) = 1

, then

\lim_{x \to 1}

f\left(x\right) is equal to

Options

A $1$
B $3$
C $2$
D $4$

Correct answer

C. $2$

Step-by-step solution

\lim_{x \to 1} f\left(x\right) = \lim_{x \to 1}\dfrac{g^{'} ( x )2\sqrt{g\left(x\right)}}{12\sqrt{x}}

= \lim_{x \to 1}\dfrac{g^{'}\left(x\right). \sqrt{x}}{g\left(x\right)} = \dfrac{g^{'}\left(1\right). \sqrt{1}}{g\left(1\right)} = 2

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