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Lim ex-e-x-2x

x-sinx As x tends to zero

a)1

b)-1

c)2

d)0

Plz explain.......

Srinath Gandhi , 14 Years ago
Grade
anser 2 Answers
Krishna Kant Tiwari

Last Activity: 14 Years ago

apply l-hospital's rule

ex+e-x-2/(1-cosx)

again apply l-hospital's rule

ex-e-x/sinx 

again apply l-hospital's rule

ex+e-x/cosx

put the limit x tend to zero

we get answer as 2

Answer:2

abhishek ganguly

Last Activity: 14 Years ago

Since it is 0/0 on putting x=0 apply L'Hospital rule  ie  differentiate numerator and denominator with respect to x

Hence we get lim x(tends to 0) (ex + e-x-2)/1-cosx

Again it is 0/0

hence differentiating again we get

lim (ex-e-x)/sinx

Again it is 0/0

so apllying l hospital rule

lim (ex+e-x)/cosx

Now put x=0

we get lim = 2

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