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Lt (x->0) xcosx – log(1+x) x 2 how to solve these kind of questions without using expansions

 Lt (x->0)     xcosx – log(1+x)  
                            x2
how to solve these kind of questions without using expansions

Grade:11

2 Answers

Vikas TU
14149 Points
5 years ago
As it is 0/0 indeterminant form solve it by applying L-Hospital 2 times.
Hence, 
=> (cosx – xsinx – 1/(1+x))/2x
=> (-sinx – sinx -xcosx + 1/(1+x)^2)/2
Put x = 0 
=> ½.
seetaram dantu
29 Points
5 years ago
what if it is not in the form of 0/0?
like cosx- log(1+x)/x2?
 
if there is an other way too, please let me know

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