`lim_(xto0) ((1+tanx)/(1+sinx))^(cosecx)` is equal to

Question

`lim_(xto0) ((1+tanx)/(1+sinx))^(cosecx)` is equal to

`lim_(xto0) ((1+tanx)/(1+sinx))^(cosecx)` is equal to
A. `underset(xto0)limf(x)` exists for `ngt0`
B. `underset(xto0)limf(x)` does not exists for `nlt0`
C. `underset(xto0)limf(x)` does not exists for any value of n
D. `underset(xto0)limf(x)` exists for any value of n

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
`underset(xto0)lim((1+tanx)/(1+sinx))^(cosecx)=underset(xto0)lim((1+tanx)^((1)/(sinx)))/((1+sinx)^((1)/(sinx)))`
`=(underset(xto0)lim((1+tanx)^((1)/(tanx)))^((1)/(cosx)))/((1+sinx)^((1)/(sinx)))`
`=(e^((1)/(cos0)))/(e)=1`

4 views Answered 2023-02-05 15:29