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Let a1, a2,......, an be fixed real numb...

Let `a_1, a_2,......, a_n` be fixed real numbers and define a function `f(x)=(x-a_(1))(x-a_(2)) ......(x-a_(n))` . What is `lim_(x rarr a_1)f(x)` ? For some `a ne a_(1),a_(2),.........a_(n)`, compute `lim_(x rarr a) f(x)` .

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Let a1, a2,......, an be fixed real numbers and define a function f(x)...

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  2. Evaluate the following limit if they exist : lim(x rarr 2) 4.

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  3. Evaluate the following limit if they exist : lim(r to 1) pir^(2) .

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  4. Evaluate the given limit : lim(x to pi) (x - 22/7)

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  5. Evaluate the following limit if they exist : lim(x rarr 2) (3-x) .

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  6. Evaluate the following limit if they exist : lim(x rarr 1) (x^3-x^2+...

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  7. Evaluate the following limit if they exist : lim(x rarr 3) ( x(x+1))...

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  8. Evaluate the following limit if they exist : lim(x rarr 0) (3x+1)/(x...

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  9. Evaluate the following limit if they exist : lim(x rarr 0) (ax+b)/(c...

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  10. Evaluate the following limit if they exist : lim(x rarr 1) (x^2+1)/(...

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  11. Evaluate the following limit if they exist : lim(x rarr 3) (x^2-4x)/...

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  12. Evaluate the following limit if they exist : lim(x rarr 2) (x^3-4x^2...

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  13. Evaluate the following limit if they exist : lim(x rarr 2) (x^2-4)/(...

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  14. Evaluate the following limit if they exist : lim(x rarr -1) (x^3-3x+...

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  15. Evaluate the following limit if they exist : lim(x rarr 0) ((x-1)^2+...

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  16. Evaluate the following limit if they exist : lim(x rarr -1) [1+x+x^2...

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  17. Evaluate the following limit : lim(x rarr 1) (x-1)/(x+1) .

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  18. Evaluate the following limit : lim(x rarr -2) (1/x+1/2)/ (x+2).

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  19. Evaluate the following limit : lim(x rarr -1) (x^2-1)/ (x+1) .

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  20. Evaluate the following limit : lim(x rarr 1) (x^3-1)/ (x-1) .

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  21. Evaluate the following limit : lim(x rarr 2) (x^3-8)/(x^2-4) .

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