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Let f(x) be twice differentiable functio...

Let `f(x)` be twice differentiable function such that `f'(0) =2`, then, `lim_(xrarr0) (2f(x)-3f(2x)+f(4x))/(x^2)`, is

A

6

B

3

C

12

D

none of these

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A
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OBJECTIVE RD SHARMA-LIMITS-Chapter Test
  1. lim(xrarr0) (3x+|x|)/(7x-|x|) , is

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  2. Let alpha,beta(alpha < beta) be the roots of the equation ax^2+bx+c=0...

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

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  4. ("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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  5. lim(xrarr0) (xtan2x -2x tan x)/((1-cos 2x)^2), is

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

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  7. 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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  8. Let f(x) be twice differentiable function such that f'(0) =2, then, li...

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  9. lim(xrarrpi//4)(1-cot ^3x)/(2-cot x-cot ^3x), is

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  10. lim(xto0) {(1)/(x3sqrt(8+x)-(1)/(2x))} is equal to

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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(xrarroo) ((1+3x)/(2+3x))^((1-sqrtx)/(1+sqrtx)), 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. The value of 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. If a=min {x^2+4x+5:x in R} and b=lim(thetato 0) (1-cos 2theta)/(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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