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If f is a continous function with int(0)...

If `f` is a continous function with `int_(0)^(x)f(t)dt to oo` as `|x|to oo`, then show that every line `y=mx` intersects the curve `y^(2)+int_(0)^(x)f(t)dt=2`

A

`-1`

B

`sqrt(2)`

C

`3`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`int_(0)^(x)g(t)dt=2-K^(2)x^(2)=2-int_(0)^(x)2K^(2)tdt`
Let `f(x)=int_(0)^(x)[2k^(2)t+g(t)]dt-2`
As, `2K^(2)t` and `g(t)` are continuous
`=[2K^(2)t+g(t)]` is also continuous
`f(0)=-2,lim_(2to oo)f(x)to oo`
As `f(x)` changes its sign
`impliesf(x)=0` for some `xepsilonR` & `AA KepsilonR`
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