What are a,b and c if$$\lim_{x \rightarrow 0}(\frac{ ae ^{-x} + bcos(x) + ce ^{x} }{ xsin(x) })$$ is equal to 2.

Question

anonymous · Answer

a must be 0 - first of all

anonymous · Answer

Otherwise one will have + or - infty/0 and it diverges

anonymous · Answer

a=0

anonymous · Answer

nope

anonymous · Answer

You want any hint?

anonymous · Answer

Ok ok got it now

anonymous · Answer

take 2-nd degree taylor expansion of all three terms above the frac. line and require that the 0-th order and 1-st order combinations vanish (in the denumerat. of course)

anonymous · Answer

0-th order has the coeffs
a + c +b = 0

anonymous · Answer

ok keep it up.

anonymous · Answer

1-st order requirement is
-a + c = 0

anonymous · Answer

soo 2a + b = 0 ===>
b = -0.5 a

anonymous · Answer

Vai ze fird oder torms du not mattah , u ahsk ?

anonymous · Answer

In english

anonymous · Answer

Vell zey duh noht mahtah since the DENOMINATOR TAylor series is of 2-nd order

anonymous · Answer

what is the answer finally?

anonymous · Answer

More precisely - the Biggest terms which will define the size of denominator
are x*x because sin x ~ x near 0

anonymous · Answer

Any combination such that a = c
uhnd
b = -2a

anonymous · Answer

Exactly, You are smart.
THANKS

anonymous · Answer

no bettah anser 
vill be a Medal

anonymous · Answer

actually a = 1 uhnd b = -2 iz VEE AHNSAH !

anonymous · Answer

Vich lanvige duh uou mien , eggzaktlee ?

anonymous · Answer

thx 4 z mdl @Zekarias

anonymous · Answer

tx  @experimentX