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

Find (i) `underset(x to 5)(lim 6)`
(ii) `underset(x to 2)(lim x)`
(iii)` underset(x to 3)(lim [x + 2])`
(iv) `underset(x to 2)(lim 4x + 2])`

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(i) `underset(x to 5)(lim) 6 = 6` `[:' underset(x to 3)(lim) C = C` where C is any real number `]`
(ii) `underset(x to 2)(lim) x = 2` `[:' underset(x to a)(lim) x = a]`
(iii) `underset(x to 3)(lim) [x + 2] - underset(x to 3)(lim) x + underset(x to 3)(lim) 2` `[:' underset(x to oo)(lim) (f(x) + g(x)) = underset(x to a)(lim) f (x) + underset(x to a)(lim) g (x)] = 3 + 2 = 5`
(iv) `underset(x to 2) [4x + 2] = underset(x to 2)(lim) 4x + underset(x to 2)(lim)2` `[:' underset(x to oo)(lim) [f(x) + g(x)] = underset(x to a)(lim) f(x) + underset(x to a)(lim) g(x)]`
`= 4 underset(x to 2)(lim) x + underset(x to 2)(lim) 2` `[:' underset(x to a)(lim) lambda f(x) = lambda underset(x to a)(lim) f(x), "where" lambda "is constant"]`
`= 4 (2) + 2 [:' underset(x to a) x = a]`
= 10
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AAKASH INSTITUTE-LIMITS AND DERIVATIVES -Example
  1. For the function f(x) = 2. Find lim(x to 1) f(x)

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  2. Find lim(x to 0) f(x), where f(x) = {{:(x -1,x lt 0),(0,x = 0),(x =1,...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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