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Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2...

Let `L_(1) = lim_(xrarr0^(+)) (int_(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx)`, then identify the correct option(s).

A

`L_(1) = 4`

B

`L_(1) + L_(2) = 8`

C

`L_(1) + L_(2) = 0`

D

`|L_(2)| = |L_(1)|`

Text Solution

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The correct Answer is:
A, C, D
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - III
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  2. Let f : R rarr R be defined as f(x) = int(-1)^(e^(x)) (dt)/(1+t^(2)) +...

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  3. If a,b in R^(+) then find Lim(nrarroo) sum(k=1)^(n) ( n)/((k+an)(k+bn...

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  4. Let f(x) = int(x)^(x+(pi)/(3))|sin theta|d theta(x in [0,pi])

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  5. If f(x) in inegrable over [1,2] then int(1)^(2) f(x) dx is equal to :

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  6. Let I(n) = underset(0)overset(1//2)int(1)/(sqrt(1-x^(n))) dx where n ...

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  7. If f(x) = 2^(|x|) where [x] denotes the fractional part of x. Then wh...

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  8. Let f(x) = int(0)^(x)|2t-3|dt, then f is

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  9. Let f(x) = int(0)^(pi)(sinx)^(n) dx, n in N then

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  10. Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R, then

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  11. Let I(n) = int(0)^(pi)(sin^(2)(nx))/(sin^(2)x)dx, n in N then

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  12. Let f(x) be a continuous function and I = int(1)^(9) sqrt(x)f(x) dx, t...

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  13. Let A = int(1)^(e^(2))(lnx)/(sqrt(x))dx, then

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  14. Let f(a,b) = int(a)^(b)(x^(2)-4x+3)dx, (bgt 0) then

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  15. Let I = int(2)^(oo)((2x)/(x^(2)+1)- (1)/(2x+1)) dx & I is a finite r...

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  16. Let L(1) = lim(xrarr0^(+)) (int(0)^(x^(2)) sinsqrt(t)dt)/(x-sinx), the...

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  17. lim(nrarroo) ((1^(k)+2^(k)+3^(k)+"......"n^(k)))/((1^(2)+2^(2)+"....."...

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  18. Let T(n) = sum(r=1)^(n) (n)/(r^(2)-2r.n+2n^(2)), S(n) = sum(r=0)^(n)(n...

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  19. A function f(x) satisfying int(0)^(1) f(tx)dt=n f(x), where xgt0, is

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  20. Find the area bounded by y=sin^(-1)x ,y=cos^(-1)x ,and the X-axis.

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