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If lim(x to 3) (x^(n) - 3^(n))/(x - 3) ...

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

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To solve the limit problem, we start with the given expression: \[ \lim_{x \to 3} \frac{x^n - 3^n}{x - 3} = 1458 \] We can use the limit formula for the difference of powers, which states: ...
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -Example
  1. Evaluate lim(x to 3) (x^(7) - 2187)/(x^4 - 81)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Find the derivative of the following functions using first principle o...

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  18. Find the derivative of the following functions using first principle o...

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  19. Find the derivative of the following functions (i) x^(3) + cos x + ...

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  20. Find the derivative of the following functions. (i) (x^(2) tan x) ...

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