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If f (9) = 9, f '(9) = 1, then lim(x rar...

If f (9) = 9, f '(9) = 1, then `lim_(x rarr 9) (8-sqrt(f(x)))/(3-sqrtx)` =

A

3

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1

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0

D

2

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Find lim_(x rarr 0) f(x) , where f (x) =|x|-5.

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Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is a. ((12)/(25),(-9)/(25)) b. ((12)/(25),(9)/(25)) c. ((16)/(25),(-8)/(25)) d. ((24)/(25),(-7)/(25))

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If the function f (x) satisfies lim_(x rarr 1)(f(x)-2)/(x^2-1)=pi , evaluate lim_(xrarr1)f(x) .

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MODERN PUBLICATION-PROBABILITY -EXERCISE
  1. lim(x rarr pi/2) [sin x] is :

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  2. The value of lim(x rarr 0) (sin bx)/(sin ax) is equal to:

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  3. lim(x rarr pi/2) (cotx-cos x)/(pi-2x)^3 equals :

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  4. Let f(x)= (sqrt(x+3))/(x+1), then the value of lim(x rarr -3^-) f(x) i...

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  5. Let alpha and beta be the roots of ax^2 + bx +c =0, then underset(x to...

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  6. If f (9) = 9, f '(9) = 1, then lim(x rarr 9) (8-sqrt(f(x)))/(3-sqrtx) ...

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  7. lim(n rarr oo)(3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n)) =

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  8. Discuss the continuity of the function f(x) = underset(n rarr oo)(lim)...

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  9. lim(x rarr 0) (e^(x^2)-cosx)/x^2 =

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  10. The value of lim(nto oo)(a^(n)+b^(n))/(a^(n)-b^(n)), (where agtb) is

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  11. Events A, B, C are mutually exclusive events such that P (A) = (3x+1)/...

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  12. Two numbers are selected randomly from the set S={1,2,3,4,5,6} without...

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  13. If three distinct number are chosen randomly from the first 100 natura...

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  14. Three houses are available in a locality. Three persons apply for the ...

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  15. Two aeroplanes I and II bomb a target in successions. The probabilitie...

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  16. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. ...

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  17. Let L=lim(xto0)(a-sqrt(a^(2)-x^(2))-(x^(2))/4)/(x^(4)),agt0. If L is f...

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  18. If the mean deviation about the median of the numbers: a, 2a,.......,...

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  19. Let f: R rarr [10,oo) be such that lim(x rarr 5)f(x) exists and lim(x...

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  20. A scientist is weighting each of 30 fishes. Their mean weight worked o...

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