If lim x → 0 ( 1 + a sin x ) c o s e c x = 3 , then a is Options: A . &nbsp In 2 B . &nbsp In 3 C . &nbsp In 4 D . &nbsp e 3

Answer: Option B : B 3 = lim x → 0 ( 1 + a sin x ) c o s e c x [ 1 ∞ f o r m ] ⇒ lim x → 0 e c o s e c x . a sin x = e a ∴ e a = 3 ⇒ a = log e 3 = l n 3.

If limx→0(1+asinx)cosecx=3, then a is

Discussion Forum : Limits Continuity And Differentiability

Question -

If $lim x \to 0 (1 + a sin x)^{c o s e c x} = 3,$ then a is

Options:

A . In 2

B . In 3

C . In 4

D .

e^{3}

Answer: Option B
:
B

3 = lim x \to 0 (1 + a sin x)^{c o s e c x}

[1^{\infty} f o r m] \Rightarrow lim x \to 0 e^{c o s e c x . a sin x} = e^{a}

∴ e^{a} = 3 \Rightarrow a = {log}_{e} 3 = l n 3.

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Discussion Forum : Limits Continuity And Differentiability

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