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Lt(x rarr 0) int(0)^(x) ((sin^(2) 4t +t^...

`Lt_(x rarr 0) int_(0)^(x) ((sin^(2) 4t +t^(2))dt)/(x^(3))`=

A

0

B

`(4)/(3)`

C

`(17)/(3)`

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-DEFINITE INTEGRAL-Problem set (5) (Multiple Choice Questions)
  1. The value of Lt(x rarr 0)(int(0)^(x^(2)) sec^(2) tdt)/(x sin x) is

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  2. lim(x rarr 0)(int(0)^(x^(2)) (sin sqrt(t) dt))/(x^(3)) is equal to

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  3. Lt(x rarr 0) int(0)^(x) ((sin^(2) 4t +t^(2))dt)/(x^(3))=

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  4. If f(x)= int(x^(2))^(x^(4)) sin sqrtt dt, then f'(x) equals

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  5. Let f(x)= int(1)^(x) sqrt(2-t^(2)) dt. Then the real roots of the equa...

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  6. lim(x rarr 0) (1)/(x) [int(y)^(a) e^(sin^(2)t) dt- int(x+y)^(a) e^(sin...

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  7. The equation of tangent to the curve y= int(x^(2))^(x^(3)) (dt)/(sqrt(...

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  8. If x= int(0)^(y) (dt)/(sqrt(1+9t^(2))) then (dy)/(dx) is equal to

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  9. If f(x)= int(x)^(x^(2)) (dt)/(1+ t^(3)), then f'(2)=

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  10. If f(x) = int(1//x^(2))^(2) cos sqrtt dt then f'(1) is equal to

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  11. If int(sin x)^(1) t^(2) f(t) dt =1- sin x, x in (0, (pi)/(2)) then f((...

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  12. If f(x)= int(x^(2))^(x^(3)) (dt)/(log t), x gt 0 then

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  13. Let f:(0, oo) in R and F(x) =underset(0)overset(x) int f(t) dt. If F(x...

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  14. If int(0)^(t^(2)) xf (x) dx= (2)/(5) t^(5), then f(4/25)=

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  15. The integral int(0)^(2) (|x+2|)/(x+2)dx is equal to

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  16. int(-3)^(3) (x-4)/((|x-4|))dx=

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  17. The value of overset(sin^(2)x)underset(0)int sin^(-1)sqrt(t)dt+overs...

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  18. If int(pi//3)^(x) sqrt(3-2sin^(2)u) du + int(0)^(y) cos t dt= 0, then ...

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  19. The points of extremum of the function F(x)= int(1)^(x) e^(-t^(2)) (1-...

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  20. The points of extemum of f(x)= int(0)^(x^(2)) (t^(2)- 5t +4)/(2+e^(t))...

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