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please solve the following limit limit (x-->0) [(1+tanx)/(1+sinx)]"cosec x thanks in advance

please solve the following limit


limit (x-->0) [(1+tanx)/(1+sinx)]"cosec x


thanks in advance

Grade:

1 Answers

jitender lakhanpal
62 Points
9 years ago

hi ravi

the answer is 1 given below is explanation

the function is of form a / b   you can write it as limit (x-->0) (1+tanx)^cosecx / (1+sinx)^1/sinx

now in denominator x tends to 0 so sinx will also tend to 0

so it will be in form lim x tend to 0 (1+x)^(1/x) and is equal to e

similarly in numerator (1+ sinx/cosx)^cosx/sinx *cosx is also of above form so e

 

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