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The value of underset(x -> (pi)/(2))(lim...

The value of `underset(x -> (pi)/(2))(lim) ({1 - tan (x/2)}{1-"sin"x})/({1 + tan (X/2)}(pi - 2x)^(3))` equals

A

0

B

`(1)/(32)`

C

`oo`

D

`(1)/(8)`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -Section - B
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  2. Evaluate the following limits : Lim(theta to pi/2 ) (sec theta - ta...

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

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  4. The value of lim(x to 0) ((1)/(x^(2)) - cot x) equals

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  5. Evaluate the limit: ("lim")(hvec0)[1/(h(8+h)^(1/3))-1/(2h)]

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  6. underset(xtooo)lim[sqrt(x+sqrt(x+sqrt(x)))-sqrt(x)] is equal to

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  7. lim(x to 2^+) (([x]^(3))/(3) - [(x)/(3)]^(3)) is where [x] represents ...

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  8. underset(x to 2)(Lt) {[x - 2] + [2 - x] - x} = where [.] represents gr...

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  9. If {x} denotes the fractional part of x, then lim(x to 0) ({x})/(tan ...

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  10. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

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  11. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0. Then ...

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  12. underset(x to 0)(Lt) (sqrt(1 - cos 2 x))/(sqrt(2)x) =

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  13. The value of lim(x to 0) ("sin" alpha X - "sin" beta x)/(e^(alphax) -...

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  14. The value of underset(x -> (pi)/(2))(lim) ({1 - tan (x/2)}{1-"sin"x})/...

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  15. The value of lim(x to 0) ((4^(x) - 1)^(3))/("sin"(x)/(4) log (1 + (x^...

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  16. If 0 lt alpha lt beta then lim(n to oo) (beta^(n) + alpha^(n))^((1)/(n...

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  17. If lim(xto0)({(a-n)nx-tanx}sin nx)/(x^(2))=0, where n is non zero real...

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  18. lim(x + 5^(+)) (x^(2) - gx + 20)/(x - [x]) is equal to

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  19. lim(x to 0) ("sin"2X)/(2 - sqrt(4 - x)) is

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  20. lim(x to 0) (1 - cos x)/(x sqrt(x^(2))

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