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If 3x+2y=1 is a tangent to y=f(x) at x=1...

If `3x+2y=1` is a tangent to `y=f(x)` at `x=1//2`, then `lim_(xrarr0) (x(x-1))/(f((e^(2x))/(2))-f((e^(-2x))/(2)))`

A

`1//3`

B

`1//2`

C

`1//6`

D

`1//7`

Text Solution

Verified by Experts

The correct Answer is:
A
Slope of `3x+2y=1" is "(-3)/(2)`
`rArr" "f'((1)/(2))=(-3)/(2)`
`therefore" "underset(xrarr0)(lim)(x(x-1))/(f((e^(2x))/(2))=f((e^(-2x))/(2)))`
`=lim(2x-1)/(e^(2x).f'((e^(2x))/(2))+e^(-2x)f'((e^(-2x))/(2)))`
`=(-1)/(f'((1)/(2))+f'((1)/(2)))=(1)/(3)`
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