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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`A. `-1`B. `sqrt(2)`C. `3`D. `1` |
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Answer» Correct Answer - 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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