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The integer n for which the lim(x to 0...

The integer `n` for which the
`lim_(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x)-(x^(3))/2)/(x^(n))` is a finite non-zero number is

A

2

B

3

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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FIITJEE-TIPS-ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)
  1. Which of the following is differentiable in the interval (1, 2)?

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  2. If f(x)=lim(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(...

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  3. The integer n for which the lim(x to 0)(cos^(2)x-cosx-e^(x)cosx+e^(x...

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  4. If f(x)=(tan(pi/4+(log)e x))^((log)x e) is to be made continuous at x=...

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  5. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

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  6. If f is twice differentiable such that f"(x)=-f(x) f'(x)=g(x),h'(x)=...

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  7. lim(x->0) (tan^2[x])/([x]^2), where [] represents greatest integer fun...

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  8. lim(xrarr1^(+))(log(sqrt2)sqrt2x)^(1/({x})) where [ ] represents great...

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  9. The value of lim(xto(pi)/4)(4sqrt(2)-(cosx+sinx)^(5))/(1-sin2x) is

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  10. lim(xrarrpi)([sinx]+x) is

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  11. The slope of the tangent of the curve y=int0^x (dx)/(1+x^3) at the poi...

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  12. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

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  13. The difference between the greatest and the least values of the functi...

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  14. Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increas...

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  15. If f(1)(x)=2x, f(2)x(=3 sin x-x cos x, for x in (0, (pi)/(2))

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  16. Let f(x)=x^3+kx^2+5x+4sin^2x be an increasing function on x in R. Th...

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  17. Let g'(x)gt 0 and f'(x) lt 0 AA x in R, then

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  18. If x1 and x2 are abscissae of two points on the curve f(x) = x - x^2 i...

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  19. f(x)={ax^2+bx+c, |x| > 1 x+1, |x| <= 1. If f(x) is continuous for all ...

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  20. Function g(x)=int- 3^xsint(1/2-cost)dt where 0 < x < 2pi, has

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