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If f(x)=(2x+3sinx)/(3x+2sinx),x!=0 is co...

If `f(x)=(2x+3sinx)/(3x+2sinx),x!=0` is continuous at `x=0` , then find `f(0)dot`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
1`f(0)=LHL=RHL`
`f(0)=lim_(x->0^+)f(x)=lim_(x->0^+)(2x+3sinx)/(3x+2sinx)`
`=lim_(x->0^+)(2+3cosx)/(3-2cosx)`
`=(2+3)/(3+2)=5/5=1`
f(0)=1.
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