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Let `f(x)` be a twice-differentiable function and `f''(0)=2.` Then evaluate `underset(xto0)lim(2f(x)-3f(2x)+f(4x))/(x^(2)).`

A

6

B

3

C

12

D

none of these

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A
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. lim(xrarr oo) (int(0) ^(2x)xe^(x^(2))dx)/(e^(4x^2))

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  2. Evaluate underset(xto0)lim(3x+|x|)/(7x-5|x|).

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  3. Let alpha, beta (a lt b) be the roots of the equation ax^(2)+bx+c=0. I...

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  4. Given that lim(nto oo) sum(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1...

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  5. ("lim")(xvec0)((1^x+2x+3^x++n^x)/n)^(1//x)i se q u a lto (n !)^n (b)...

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  6. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

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  7. If lim(xrarroo) {ax-(x^2+1)/(x+1)}=b , a finite number, then

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  8. If f(1) =g(1)=2, then lim(xrarr1) (f(1)g(x)-f(x)g(1)-f(1)+g(1))/(f(x)-...

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  9. Let f(x) be a twice-differentiable function and f''(0)=2. Then evaluat...

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  10. Evaluate : ("lim")(xvecpi/4)(1-cot^3x)/(2-cotx-cot^3x)

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  11. lim(xto0) (1)/(x^12){1-cos (x^2/2)-cos (x^4/4)+cos (x^2/2) cos (x^4/4)...

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  12. The value of lim(x to oo)((1+3x)/(2+3x))^((1-sqrt(x))/(1-x)) is

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  13. lim(xrarr oo) ((3x^2+2x+1)/(x^2+x+2))^((6x+1)/(3x+1)) , is equal to

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  14. The value of lim(xrarr0) (3sqrt(1+sinx )-3sqrt(1-sinx))/(x), is

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  15. Evaluate: ("lim")(h->0)((a+h)^2sin(a+h)-a^2sina)/h

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  16. lim(h -> 0) (sin(a+3h)-3sin(a+2h)+3sin(a+h)-sina)/h^3 =

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  17. Let a=min{x^(2)+2x+3,x epsilonR} and b=lim(x theta to 0)(1-cos theta)/...

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  18. If lim(xrarr0) (log (3+x)-log (3-x))/(x)=k, the value of k is

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  19. If f(x)={sinx ,x!=npi,n in I2,ot h e r w i s e g(x)={x^2+1,x!=0,4,x=...

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  20. If lim(xrarr0) (x(1+acos x)-bsin x)/(x)=1, then a-b, are

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