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Suppose lim(xrarr0)(int(0)^(x)(t^(2) dt)...

Suppose `lim_(xrarr0)(int_(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx)=l`,
`p in N, p ge 2,a gt gt 0,rgt 0 and b ne 0`
If `p=3 and l=1,` then the value of 'a' is equal to

A

8

B

3

C

6

D

`3//2`

Text Solution

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The correct Answer is:
A
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Passage Based Questions)
  1. Suppose lim(xrarr0) (int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- si...

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  2. Suppose lim(xrarr0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sinx...

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  3. Suppose lim(x to 0)(int(0)^(x)(t^(2) dt)/((a+t^(r))^(1//p)))/(bx- sin...

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  4. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

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  5. Suppose f(x) and g(x) are two continuous function defined for 0 le xl...

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  6. Suppose f(x) and g(x) are two continuous functions defined for 0<=x<...

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  7. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

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  8. Evaluate int (0)^(1) 3x^2 dx

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  9. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

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  10. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

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  11. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

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  12. f(x)=int(0)^(x) (4t^(4)-at^(3)) dt and g(x) is quadratic satifying g(...

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  13. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

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  14. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

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  15. Let y= int(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)...

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  16. Check the injectivity and surjectivity of the function sinx.

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  17. The value of int(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] den...

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