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# lim x → 0  (x cosx - log (1+x) )/x2 is equal to?

Grade:12th Pass

## 2 Answers

jitender lakhanpal
62 Points
9 years ago

Dear aditi

 lim x → 0  (x cosx - log (1+x) )/x2 cosx = 1 - x2/2! +x4 / 4! ............ x cosx  = x - x3 /2! + x5/4!..........

log (1+x) = x -x2/2 + x4/2...........

so put the above expansion in the limits we get the limit 1/2

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santhanagopalan raghavan
33 Points
9 years ago

simplest way is to use l-hospitals rule.

d^n(numerator)/d^n(denominator) until 0/0 form is removed.then substitute to obtain the limit.

(cosx - xsinx - 1/(1+x))/2x        Now since 0/0 form persists again differentiate

(-sinx - sinx -xcosx + 1/(1+x^2))/2     put x=0 to obtain the limit as,1/2

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