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lim(x rarr 0) (tan [e^(2)]x^(2)-tan[-e^(...

`lim_(x rarr 0) (tan [e^(2)]x^(2)-tan[-e^(2)]x^(2))/(sin^(2)x)` equals :

A

0

B

8

C

15

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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MODERN PUBLICATION-LIMIT AND CONTINUITY -MULTIPLE CHOICE QUESTIONS(LEVEL - II )
  1. lim(x rarr pi//3) (2 sin (x-pi//3))/(1-2 cos x) equals :

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  2. Let f(x) = {{:(x (sin 1//x + sin (1//x^(2))),,x ne 0),(0,,x = 0):} The...

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  3. lim(x rarr 0) (tan [e^(2)]x^(2)-tan[-e^(2)]x^(2))/(sin^(2)x) equals :

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  4. If lim(x rarr 0) (1+px)^(q//x) = e^(4), where p, q, in N, then :

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  5. Let f(x) = 3x^(10) - 7x^(8) + 5x^(6) - 21x^(3) + 3x^(2) - 7. Then lim(...

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  6. Let f(x) = lt x gt^("*"), where lt x gt^("*") is the distance from x t...

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  7. lim(x rarr 2^(+)) (([x]^(3))/(3) - [(x)/(3)]^(3)) equals :

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  8. If the function f(x) = [((cos x)^(1//x),x ne 0),(k,x = 0):} is continu...

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  9. Let f(x) = |x| "cos" (1)/(x) + 15x^(2), x ne 0, = k, x = 0, then f(x...

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  10. If lim(x rarr a^(+)) f(x) = l = lim(x rarr a^(-)) g(x) and lim(x rarr ...

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  11. The following are continuous on (0, pi) :

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  12. The value of b for which the function : f(x) = {{:(5x-4,"if",0lt x le ...

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  13. Let f(x) = [{:(5^(1//x),x lt 0),(lambda[x],x le 0","lambda in R):}, th...

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  14. Let f(x) = [{:((g(x) - g(a))/(x-a),x ne 0),(g'(a),x = a):}, where g is...

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  15. Let f(x) = {{:(1,x le -1),(|x|,-1 lt x lt 1),(0,x ge 1):}, then :

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  16. The function f(x) = [x] is :

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  17. Let f(x) = (1 - cos px)/(x sin x), where x ne 0 and f(0) = (1)/(2). If...

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  18. Let f(x) = (1-sin x)/((pi - 2x)^(2)),"where x" ne pi//2 and f(pi//2) =...

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  19. Let f(x) = (tan (pi//4-x))/(cot 2x)"for x" ne pi//4, then for f to be ...

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  20. Let f(x) = [{:((x^(2))/(a),0 le x lt 1),(a,1 le x lt sqrt(2)),((2b^(2)...

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