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  • Can someone explain - Limit , continuity and differentiability - JEE Main-8

\lim_{x\rightarrow \pi /4}\left ( \frac{\sin ( \tan (x-\pi /4))}{\tan (x-\pi /4)} \right )  equals 

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Answers (1)

best_answer

As we have learned

Condition for Trigonometric limit -

\lim_{x\rightarrow a}\:\:\:\frac{sin(x-a)}{x-a}=1

It\:must\:be\:\frac{sin(angle)}{(angle)_{(in\:radian)}}

- wherein

ex:-

\lim_{x\rightarrow 0}\:\:\frac{sinx}{x}=\frac{\pi}{180}

 

 When x\rightarrow \pi /4  then x- \pi /4\rightarrow 0\Rightarrow \tan (x-\pi /4)\rightarrow 0

Let \tan (x-\pi /4)=h

\Rightarrow \frac{\sin (\tan (x-\pi /4))}{\tan (x-\pi /4)}= \frac{\sin h }{h}  when h\rightarrow 0

\lim_{h\rightarrow 0}\frac{\sin h }{h}=1

 

 

 

 


Option 1)

-1

Option 2)

0

Option 3)

1

Option 4)

2

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Himanshu

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