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Evaluate lim(x to 2) [4x^(2) + 3x + 9]...

Evaluate `lim_(x to 2) [4x^(2) + 3x + 9]`

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The required limits are all limits of some polynominal function. Hence, the limits are the values of the function at the prescirbed points.
We have, `underset(x to 2)(lim) [4x^(2) + 3x + 9] = 4(2)^(2) + 3(2) + 9 = 4(4) + 6 + 9 = 31`
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AAKASH INSTITUTE-LIMITS AND DERIVATIVES -Example
  1. Find lim(x to 0) f(x), where f(x) = {{:(x -1,x lt 0),(0,x = 0),(x =1,...

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  2. Find (i) underset(x to 5)(lim 6) (ii) underset(x to 2)(lim x) (iii...

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  3. Evaluate lim(x to 2) [4x^(2) + 3x + 9]

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

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  5. Evaluate lim(x to p) (sqrt(1 + x) + sqrt(1 - x))/(1 - x)

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  6. Evaluate lim(x to 4) (x^(2) - 7x + 12)/(x^(2) - 16)

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  7. Evaluate, lim(x to 2) (x^(3) - 8)/(x^(2) - 4)

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  8. Evalutate lim(x to 4)((x^(2) - x - 12)^(18))/((x^(3) - 8x^(2) + 16x)^(...

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  9. Evaluate underset(x to 1) (X - 1)/(2x^(2 - 7x + 5)

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

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

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

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

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

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

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

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

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

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

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

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