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lim(x->0) (e^x +e^-x +2 cos x -4)/x^4 is...

`lim_(x->0) (e^x +e^-x +2 cos x -4)/x^4` is equal to

A

0

B

1

C

`1/6`

D

`-1/6`

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-LEVEL 2
  1. If lim(xtooo)((x^(2)+1)/(x+1)-ax-b)=0, find the values of a and b.

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  2. ("lim")(xvecoo)1/(1+nsin^2n x) i s equal to (a)-1 (b) 0 (c) 1 (d) ...

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  3. lim(x->0) (e^x +e^-x +2 cos x -4)/x^4 is equal to

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

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  5. The value of lim(x->oo)(1+1/x^n)^x,n>0 is

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  6. Let f and g be differentiable functions satisfying g'(a) = 2 g(a) = b ...

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  7. Evaluate: ("lim")(n→oo)(n^p sin^2(n !))/(n+1)

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  8. lim(xto oo)(x/(1+x))^(x) is

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  9. If 0 lt alpha lt beta then underset(n to oo)(lim) (beta^(n) + alpha^(n...

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  10. the value of lim(n->oo) {1/(n^3+1)+4/(n^3+1)+9/(n^3+1)+..................

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  11. lim(n to oo)sum(r=1)^(n)cot^(-1)(r^(2)+3//4) is (a) 0 (b) tan^(-1)1 (...

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  12. Evaluateunderset(xto pi//4)lim(2-tanx)^(1//1n(tanx))

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

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  14. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  15. lim(xto0)((e^(x)-1)/x)^(1//x)

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  16. If [.] denotes the greatest integer function then lim(x->oo)([x]+[2x]...

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  17. ("lim")(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1))i se q u a lto ...

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  18. lim(x to oo) (( 1+x+x^(3)))/((ln x)^(3)) is equal to

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  19. int cot^6x cosec^2xdx

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  20. underset(xtooo)lim(e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

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