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prove: limit (x) tends to 0 ((sinlog(1+x)/x))=1

prove:


limit (x) tends to 0 ((sinlog(1+x)/x))=1

Grade:11

2 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
12 years ago

Dear Abhik

this is 0/0 form apply L hospital rule

differentiate wrt x

[coslog(1+x)]/(1+x)

put x=0

coslog1/1

cos0= 1

All the best.

AKASH GOYAL

AskiitiansExpert-IITD

 

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vikas askiitian expert
509 Points
12 years ago

lim x->0 sinlog(1+x)/x

 at x=0 ,  0/0 form comes so we can use L holpital rule

        differentiating numerator and denominator

after differentiating

limx->0 coslog(1+x) /1+x

        =coslog1/1

        =cos0=1

hence proved

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