If" f, is a continuous function with `int_0^x f(t) dt->oo` as `|x|->oo`then show that every line `y = mx` intersects the curve `y^2 + int_0^x f(t) dt = 2`

Options

A. `-1`
B. `sqrt(2)`
C. `3`
D. `1`

Answer

A, B, C, D

Explanation

`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`