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Evaluate lim(x to sqrt(2)) (x^(9) - 3x^...

Evaluate `lim_(x to sqrt(2)) (x^(9) - 3x^(8) + x^(6) - 9x^(4) - 4x^(2) - 16x + 84)/(x^(5) - 3x^(4) - 4x + 12)`

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To evaluate the limit \[ \lim_{x \to \sqrt{2}} \frac{x^9 - 3x^8 + x^6 - 9x^4 - 4x^2 - 16x + 84}{x^5 - 3x^4 - 4x + 12}, \] we will follow these steps: ...
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -Example
  1. Evaluate the following limits : Lim(xto1) (x-1)/(2x^(2)-7x+5)

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  2. Evaluate lim(x to 1) ((1)/(x^(2) + x - 2) - (x)/(x^(3) - 1))

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  3. Evaluate lim(x to sqrt(2)) (x^(9) - 3x^(8) + x^(6) - 9x^(4) - 4x^(2) ...

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  4. Evaluate : underset(X to 2) (x^(8) - 256)/(x - 2)

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  5. Evaluate lim(x to 3) (x^(7) - 2187)/(x^4 - 81)

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  6. Evaluate lim(x to a) ((x + 3)^(7//5) - (a + 3)^(7//5))/(x - a)

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  7. If lim(x to 3) (x^(n) - 3^(n))/(x - 3) = 1458 and n in N, find n.

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  8. If lim(x to a) (x^(7) + a^(7))/(x + a) = 7, find the value of a.

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  9. If lim(x to 1) (x^(3) - 1)/(x - 1) = lim(x to k) (x^(4) - k^(4))/(x^...

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  10. Evaluate lim(x to 0) (sqrt(x + 2) - sqrt(2))/(x)

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  11. Evaluate lim(x to 0) ("sin" 4x)/(6x)

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  12. Evaluate lim(x to 0) ("sin"^(2) (3x//2x))/(x)

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  13. Evaluate lim(x to0 ) ("sin" 3x)/("sin" 6x)

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  14. Evaluate the following limits : Lim(x to 0) (1- cos x)/(x^(2))

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  15. Evaluate lim(x to 0) (tan x + 4 tan 2x - 3tan 3x)/(x^(2) tan x)

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  16. Evaluate lim(x to (pi)/(4)) (1 - tanx)/(x - (pi)/(4))

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  17. Let f be a real-valued function defined by f(x) = 3x^(2) + 2x + 5 Find...

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  18. Find the derivative of the following functions from the first principl...

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  19. Find the derivative of the following functions from the first principl...

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  20. Find the derivative of the following functions from first principle (i...

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