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Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^...

Let `L=("lim")_(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i t e ,t h e n` `a=2` (b) `a=1` `L=1/(64)` (d) `L=1/(32)`

A

`a=2,L=(1)/(64)`

B

`a=1,L=(1)/(64)`

C

`A=3,L=(1)/(32)`

D

`a=1,L=(1)/(32)`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
  1. lim(xrarr0) x^2sin.(pi)/(x), is

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  2. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

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  3. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

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  4. If lim(xto oo)((x^(2)+1)/(x+1)-ax-b)=2 find the values of a and b.

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  5. Evaluate the following limits : Lim(x to oo) (sqrt(x^(2)+1)-root3(x^...

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  6. lim(xrarr0) (e^(x^(2))-cosx)/(x^2) is equal to

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  7. Write the value of (lim)(x->-oo)(3x+sqrt(9x^2-x))

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  8. underset(xrarr(pi)/(4))(lim)(int(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/...

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  9. The value of underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))...

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  10. value of lim(x->0)(1-cos^3x)/(xsinx*cosx) is

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  11. lim(xrarr1)(sqrt1-cos2(x-1))/(x-1), is

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  12. Evaluate the following limits (i) lim(x to (pi)/(2)) tan^(2) x [sqr...

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  13. The value of lim(xrarr 0) (1-cos(1-cos x))/(x^4) is equal to

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  14. The value of lim (xto0) (cos (sin x )- cos x)/(x ^(4)) is equal to :

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  15. The value of underset(xto1)lim(2-x)^(tan((pix)/(2))) is

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  16. The value of lim(xrarroo) ((3x-4)/(3x+2))^(((x+1)/3)) is

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  17. lim(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to

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  18. The value of lim(xrarr0) ((1+tanx)/(1+sin x))^(cosec x) , is

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  19. lim(x rarr 0)((5x^2+1)/(3x^2+1))^(1//x^2)

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  20. Evaluate: ("lim")(n→oo)x[tan^(-1)((x+1)/(x+2))-tan^(-1)(x/(x+2))]

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