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  • Need explanation for: - Limit , continuity and differentiability - JEE Main-6

\lim_{x\rightarrow \pi /2} \frac{\sin ^{2}x+ \sin x -4}{\tan (x/2)+ \sin x}  equals

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Answers (1)

best_answer

As we have learned

Evaluation of limits : (algebraic limits) : (Method of direct substitution) -

\lim_{x\rightarrow a}f(x)\:defines\:by\:direct\:x=a


ex: \:\lim_{x\rightarrow 1}\:\frac{x^{2}+x+1}{x^{2}+x-1}=3

- wherein

Means at  x = a  f(x) defined.

 

 \lim_{x\rightarrow \pi /2} \frac{\sin ^{2}x+\sin x-4}{\tan (x/2)+\sin x}=\frac{\sin^{2}\pi /2+\sin\pi /2-4}{\tan \pi /4+\sin \pi /2}

\frac{1^{2}+1-4}{1+1}=\frac{-2}{2}=-1

 

 

 

 

 


Option 1)

-1

Option 2)

0

Option 3)

1

Option 4)

2

Posted by

Himanshu

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