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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-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f : [1/2, 1] rarr R (the set of the all real numbers) be a positiv...

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  2. For a in R (the set of all real numbers), a ne = - 1, lim(nrarroo)((...

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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) rArr R be given f(x) = underset(1/x)overset(x)e^((1+(dt...

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  5. The value of int(0)^(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)(2cosecx)^(17) dx is equal to

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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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  10. Let f : R rarr R be a function defined by f(x) ={{:([x],xle2),(0,xgt...

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

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

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

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

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

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

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

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

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

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

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