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If f(x) is the integral of (2 s...

If ` f(x) ` is the integral of ` (2 sin x - sin 2x )/(x ^ 3 ) ` , where ` x ne 0`, then find ` lim _ (x to 0) f' (x) ` .

A

0

B

1

C

-1

D

2

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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. Evaluate underset(ntooo)limncos((pi)/(4n))sin((pi)/(4n)).

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  2. Evaluate ("lim")(n→oo){cos(x/2)cos(x/4)cos(x/8)... cos(x/(2^n))}

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  3. If f(x) is the integral of (2 sin x - sin 2x )/(x ^ 3 ) , w...

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  4. Evaluate: ("lim")(xvec0)x^m(logx)^n ,m , n in Ndot

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  5. The value of lim(xrarroo) (logx)/(x^n), n gt 0, is

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  6. underset(xtoa)lim(log(x-a))/(log(e^(x)-e^(a)))

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  7. Let < an > be a sequence such that lim(x->oo)an=0. Then lim(n->oo)(a1...

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  8. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of ("l...

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  9. If f(9)=9,f^(prime)(9)=4,t h e n("lim")(nvecoo)(sqrt(f(x)-3))/(sqrt(x-...

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  10. A(i)=(x-a(i))/(|x-a(i)|),i=1,2,...,n," and "a(1)lta(2)lta(3)lt...lta(n...

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  11. lim(x -> oo) x^n / e^x = 0, (n is an integer) for

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  12. lim(xrarr0) (x)/(tan^-1x) is equal to

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  13. If f(x) =x , x<0 and f(x)=1 , x = 0, and f(x)=x^2,x>0 then lim(x->0) ...

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  14. Evaluate the following limits : Lim(x to oo) sqrt(((x+sin x)/(x- cos...

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  15. Evaluate: ("lim")(xvecoo)(1+1/(a+b x))^(c+dx),w h e r ea , b , c ,a n ...

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  16. If f'(2)=2, f''(2) =1, then lim(xrarr2)(2x^2-4f'(x))/(x-2), is

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  17. lim(xrarr0) (e^(tanx)-e^x)/(tanx-x)=

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  18. The value of lim(xrarr2^-) {x+(x-[x])^2}, is

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  19. lim(xto0) ((e^x+e^-x-2)/(x^2))^(1//x^2) is equal to

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  20. The value of lim(x->oo)(pi/2-tan^(- 1)x)^(1/x^2), is

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