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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))|dtfora l lx in [-1,2]dotIf(lim)_(xvec1)(F(x))/(G(x))=1/(14),` Then the value of `f(1/2)` is

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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f : R rarr R be a function defined by f(x) ={{:([x],xle2),(0,xgt...

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  2. If alpha = int(0)^(1)e^(9x+3tan^(-1)x)) ((12+9x^(2))/(1+x^(2)))dx wher...

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

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  4. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^4x-3tan^2x for all x in (-pi/2,...

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  5. Let f'(x) = (192x^(2))/(2+sin^(4)pix) for all x in R with f(1/2) = 0. ...

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  6. The option(s) with the values of a and L that satisfy the following eq...

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  7. Let F:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

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  8. Let F : R rarr R be a thrice differentiable function, Supose that F(...

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  9. Let F(x) = int(x)^(x^(2)+(pi)/(6))2cos^(2)t dt for all x in R and f: [...

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  10. The total number of distinct x in (0,1] for which int(0)^(x)(t^(2))/...

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  11. The value of int(-(pi)/(2))^(pi/2)(x^(2)cosx)/(1+e^(x))dx is equal to

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  12. Area of region {(x,y) in R^(2): y ge sqrt(|x+3|,)5y le x + 9 le 15}

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  13. Let f(x) = lim(nrarroo) ((n^(n)(x+n)(x+n/2)"......."(x+n/n))/(n!( x^(...

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  14. Let f: Rvec(0,1) be a continuous function. Then, which of the followin...

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  15. Let f : R rarr R be a defferentiable function such that f(0) = 0 , f(p...

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  16. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: I<(49)/(50) ...

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  17. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

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  18. If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : g^(prime)(pi/2)...

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  19. For each positive integer n, let y(n) = 1/n ((n+1)(n+2) "……"(n+n))^...

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  20. A farmer F1 has a land in the shape of a triangle with vertices at ...

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