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Evaluate underset(x to 3)(lim) (x^(3) - ...

Evaluate `underset(x to 3)(lim) (x^(3) - 7x^(2) + 15x - 9)/(x^(4) - 5x^(3) + 27 x - 27)`

A

`(2)/(9)`

B

`(9)/(2)`

C

1

D

0

Text Solution

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The correct Answer is:
A
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -SECTION - A
  1. lim(x to 0) (2 sin x - sin 2x)/(x^(3)) ie equal to

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  2. 'underset(x to 0) (sqrt(a +x) - sqrt(a))/(x sqrt(a^(2) + ax)) is equal...

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  3. Evaluate underset(x to 3)(lim) (x^(3) - 7x^(2) + 15x - 9)/(x^(4) - 5x^...

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  4. If f (x) = x^(4) + 2x^(3), them lim(x to 2) (f(x) - f(2))/(x - 2) is ...

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  5. underset(x to sqrt(2))(It) (x^(2) - 2)/(x^(2) + sqrt(2)x - 4) is equal...

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  6. lim(x to 27) (x^(1//3) + 3) (X^(1//3) - 3))/(x - 27) is equal to

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  7. lim(x to 2) (x^(3) + x^(2) + 4x + 12)/(x^(3) - 3x + 2) is equal to

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  8. lim(x to 4) (x^(2) - 16)/(sqrt(x) - 2) is equal to

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  9. Evaluate the following limits : Lim(x to 2) (x-2)/(sqrt(x)-sqrt(2))

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  10. lim(x to 0) (x)/(tan x) is equal to

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  11. The derivative of f(x) = x^(2) at x = 1 is

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  12. The derivative of f (x) = x^(2) + 2x at x = 2 is

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  13. The derivative of f(x) = "sin" 2x is

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  14. The derivative of f(x) = (sqrt(x) + (1)/(sqrt(x)))^(2) is

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  15. If Y = (1 + tan x)/(1 - tan x), then (dy)/(dx) is

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  16. The derivative of f(x) = x^(-3) (3 + 7.x) is

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  17. The derivative of f(x) = (3 x + 2 "sin" x)/(x + 5 cos x) is

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  18. The derivative of f(x) = (x + (1)/(x))^(3)

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  19. Compute the derivative of f(x)=sin^2x.

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  20. The derivative of f(x) = (x - 4)^(2) is

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