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Let f: RvecR be a continuous odd functio...

Let `f: RvecR` be a continuous odd function, which vanishes exactly at one point and `f(1)=1/2dot` Suppose that `F(x)=int_(-1)^xf(t)dtfora l lx in [-1,2]a n dG(x)=int_(-1)^x t|f(f(t))|dt`
`fora l lx in [-1,2]dot` If `(lim)_(x vec 1)(F(x))/(G(x))=1/(14),` Then the value of `f(1/2)` is

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ARIHANT MATHS-LIMITS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let alpha, beta in R such that lim(x ->0) (x^2sin(betax))/(alphax-sin...

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  2. If y=(sqrt(x) + 1/sqrt(x))^2 .Find dy/(dx)

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  3. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

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  4. The largets value of non negative integer for which lim(x->1){(-a x+si...

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  5. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

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  6. underset(xto(pi)/(2))lim(cotx-cosx)/((pi-2x)^(3)) equals

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  7. Let p=underset(xto0^(+))lim(1+tan^(2)sqrt(x))^((1)/(2x)). Then log(e)p...

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  8. lim(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to

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  9. underset(xto0)lim(sin(picos^(2)x))/(x^(2)) is equal to

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  10. lim(xto0)((1-cos2x)(3+cosx))/(x tan 4x) is equal to

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  11. If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

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  12. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

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  13. If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in ...

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  14. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)...

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  15. lim(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1)) given that f'(2)=6 and ...

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  16. lim(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero posit...

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  17. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

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  18. Let f: R->R be such that f(1)=3 and f^(prime)(1)=6. Then lim(x->0)((f...

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  19. lim(x to oo) ((x-3)/(x+2)) is equal to :

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