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Evaluate underst(x to 2)(lim) (x^(2) + 2...

Evaluate `underst(x to 2)(lim) (x^(2) + 2x - 8)/(x^(2) - 4)`

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Verified by Experts

The correct Answer is:
`(3)/(2)`
`underset(x to 2)(lim) (x^(2) + 2x - 8)/(x^(2) -4) = underset(x to 2)(lim) ((x - 2)(x + 4))/((x + 2)(x - 2))`
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AAKASH INSTITUTE ENGLISH-LIMITS AND DERIVATIVES -Try yourself
  1. Evaluate underset(x to 1)(lim) (1 + (x - 1)^(2))/(1 + x^(2))

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  2. Evaluate lim(x to a) (sqrt(x) + sqrt(a))/(x + a)

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  3. Evaluate underst(x to 2)(lim) (x^(2) + 2x - 8)/(x^(2) - 4)

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  4. Evaluate lim(x to 3) (x^(2) - 10x + 21)/(x^(2) - 9)

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

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  6. Evaluate lim(x to 2) (x^(3) - 3x^(2) + 4)/(x^(4) - 8x^(2) + 16)

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

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  8. Evaluate lim(x to 1//4) (4x - 1)/(2sqrt(x) - 1)

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

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  10. Evaluate lim(x to 2) (x^(2) - 4) [(1)/(x + 2) + (1)/(x - 2)]

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  11. Evaluate lim(x to sqrt(3)) (3x^(8) + x^(7) - 11x^(6) - 2x^(5) - 9x^(4...

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

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  13. Evaluate lim(x to 4) (x^(5) - 1024)/(x - 5)

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  14. Evaluate lim(x to 16) (x^(3//2) - 64)/(x - 16)

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  15. Evaluate underset(x to 0)(lim) (1 - x^(n) - 1)/(x)

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  16. Evaluate lim(x to a) ((x + 4)^(5//4) - (a + 4)^(5//4))/(x - a)

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  17. If lim(x to 3) (X^(n) - 3^(n))/(x - 3) = 405 and n in N Find n

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  18. If lim(x to 2) (X^(n) - 2^(n))/(x - 2) = 448 and n in N , find n

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  19. If lim(x to a) (x^(5) + a^(5))/(x + a) = 405, Find the value of a.

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  20. If lim(x to 0) (x^(9) + a^(9))/(x + a) = 9, find the value of a

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