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Value of lim(x rarr 3)(sin(e^(x-3) -1))/...

Value of `lim_(x rarr 3)(sin(e^(x-3) -1))/log(x-2)` is

A

2

B

1

C

-1

D

-2

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The correct Answer is:
B
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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If {x} denotes the fractional part of x, then lim(xrarr0)(e^{x}-1)/x i...

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  2. Consider f(x)={(x^2/|x|, x ne 0),(0, x=0):}

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  3. Value of lim(x rarr 3)(sin(e^(x-3) -1))/log(x-2) is

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  4. lim(x rarr 1) x^(1//1-x) is

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  5. lim(x rarr 0) ((1+tan x)/(1-tan x))^(1/x) is

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  6. The value of lim(x rarr 0) (int0^(x^2)sec^2tdt)/(x sinx) is :

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  7. The value of lim(x rarr 0) |cosx + sinx|/x^2 is equal to

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  8. lim(x rarr infty)(root(2)(x^2 + 1)-root(3)(x^2 + 1))/(root(4)(x^2 + 1)...

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  9. The value of a, b and c such that lim(x rarr 0) (ae^x -b cosx + ce^(...

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  10. Let f(x) = lim(n rarr infty)(sinx)^(2n), then f is

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  11. The set of all points where the function f(x)= x/(1+|x|) is differenti...

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  12. Let f(x) = (x(1+a cosx) - b sinx)/x^2, x ne 0 and f(0) = 1

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  13. If x + |y| = 2y, then y as a function of x is :

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  14. Let [x] denotes the greatest integer less than or equal to x, If (x) =...

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  15. The function f(x) = {(|x-3|, x ge 1), (x^2/4-(3x)/2+13/4, x lt1):}

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  16. Which of the following functions are continuous on (0, pi):

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  17. If f(x) = "min"{1, x^2, x^3} then :

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  18. Let f(x) be defined in [-2, 2] by f(x) = "maximum" (sqrt(4-x^2), sqr...

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  19. If lim(x rarr 0)((a^x+b^x+c^x)/3)^(lambda/x), (a, b, c, lambda gt o) i...

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  20. If f(x)=(|x|/(2 + |x|))^(2x), then

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