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raman_shadow (754)

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a function f : R R satisfies the following conditions-
1. f(x) 0 for any x  R            2. f(x+y) = f(x).f(y) for all x,y in R
3. f(x)is differentiable                4. f ' (0) = 2 (f dash zero equals 2)

                            f(x) - f(-x)            
 then [x][0]   -----------------    is
                                  x

a) 1
b) 2
c) 3
d) 4

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iitkgp_bipin (5869)

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Since f(x) is differentiable apply L'Hospitals rule :

 [x][0] {f(x) - f(-x)}/x =  [x][0] {f('x) + f'(-x)} =  {f'(0) + f(-0)}

= 2f'(0) = 4

Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur

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raman_shadow (754)

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but sir isnt that L hospital rule is applicable in either zero by zero or infinity by infinity form

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kghedriu (2333)

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Hi Raman...
in ur question,
the limit is in the form of o/o only.....
also it is differentiable, so we r using LHospital rule.
itz clear now?
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