Question

ज्ञात कीजिए : lim x tan1/x where x tends to zero
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Answer 1

lim (x)(tan1/x) x tends to zero

divide and multiply with (1/x)

=lim (x)(1/x) (tan1/x)/(1/x) x tends to zero

we know that lim (tan ( 1/x))/(1/x)=1

lim (x)(1/x) (tan1/x)/(1/x)= lim (tan1/x)/(1/x)

= 1

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Answer 2

Answer:

$\large\boxed{\sf{1}}$

Explanation:

Given a limit such that,

$\displaystyle\lim_{x\to0}x \tan( \dfrac{1}{x} )$

To evaluate the value of the given limit.

Multiply and divide the given expression by $\dfrac{1}{x}$.

Therefore, we will get,

$= \displaystyle\lim_{x\to0} \dfrac{x \tan( \dfrac{1}{x} ) }{ \dfrac{1}{x} } \times \dfrac{1}{x} \\ \\ = \displaystyle\lim_{x\to0} \dfrac{ \tan( \dfrac{1}{x} ) }{ \dfrac{1}{x} } \times x \times \dfrac{1}{x} \\ \\ \displaystyle\lim_{x\to0} \dfrac{ \tan( \dfrac{1}{x} ) }{ \dfrac{1}{x} } \times 1 \\ \\ = \displaystyle\lim_{x\to0} \dfrac{ \tan( \dfrac{1}{x} ) }{ \dfrac{1}{x} }$

But, we know that,

• $\displaystyle\lim_{m\to0} \dfrac{ \tan(m) }{m} = 1$

Therefore, we will get,

$= 1$

Hence, the required value of limit is 1.