lim x → 0 (x cosx - log (1+x) )/x2 is equal to?
lim x → 0 (x cosx - log (1+x) )/x2 is equal to?
Aditi Bhatnagar , 13 Years ago
Grade 12th Pass
Differential Calculus> limits...
2 Answers
jitender lakhanpal
Last Activity: 13 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
Last Activity: 13 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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