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Let f:[a,b]to[1,oo) be a continuous func...

Let `f:[a,b]to[1,oo)` be a continuous function and let `g:RtoR` be defined as
`g(x)={(0,"if",xlta),(int_(a)^(x)f(t)dt,"if",alexleb),(int_(a)^(b)f(t)dt,"if",xgtb):}` Then

A

`g( x)` is continuous but not differentiable at a

B

` g(x)` is differentiable on R

C

`g(x)` is continuous but not differetiable at b

D

`g(x)` is continuous and differentiable at either a or b but not both

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The correct Answer is:
A, C
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

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  2. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  3. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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  4. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

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  5. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

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  6. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

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  7. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  8. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  9. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

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  10. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

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  11. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

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  12. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

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

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  14. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

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  15. The option(s) with the values of aa n dL that satisfy the following eq...

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  16. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  17. Let F : R to R be a thrice differentiable function . Suppose that F(...

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  18. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

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  19. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

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  20. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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