Calculate the following limits using the factorization formula x" - a" = 1x - a21x"-1 + ax"-2 + a?x"-3 + . .. + a"-2x + a"-12, where n is a positive integer and a is a real number. x" - a" lim xSa х — а for any positive integer n

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A: We have given;

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A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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A: Solve by limit

Q: Calculate the following limits using the factorization formula x" - a" = 1x - a21x"-1 + ax"-2 +…

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Q: n that so that they form a rigorous assertion that lim X-

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Q: Evaluate the given limits numerically (using table of values) and graphically 1. lim2 X-2 x-2 f(x)

A: x 1.9 1.99 1.99 1.999 2.001 2.01 2.11 f(x) 3.9 3.99 3.999 4.001 4.01 4.1 4.11     limx→2x2-4x-2…

Q: lim n 4x3-4x+1 lim X→3 x-1 x²-6 lim X→-1 3x-1

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Q: Evaluate the following indicated limits. 3x +3x+5 x° + 2 1-cosx (а). lim (b). lim .3

A: (a) limn→∞3x3+3x+5x3+2 =limn→∞3+31x2+51x31+2x3=3+30+501+20=31=3 (b) limx→01-cos xx At x=0, we get…

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Q: 3. Determine the following limit. () 2-x2 – 1 lim 3. x--00

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Q: 8. Employ the dividing out technique to evaluate the following limit: 2x? +x- 6 lim - x+ 2

A: Explanation and solution is given below....

Q: Q3: Evaluate the following limits 1- lim(x2 + 5x) x-2 (x+1) 2- lim x--1 (x²+6x+5)

A: To evaluate the given limits

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Q: 1. Evaluate the following limits. x² + 3x+ 2 lim, →-1 x' +4x +3 2 а. х? — 2х lim,→2 b. Vx? +5 – 3

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Q: Evaluate the following limits. 2x – (a) lim (2+ x) |3 – 6x| 1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: Complete the following tables. * - 5 r- 3 72 – 6x + 9. r- 3 ² – 6x + 9. 2.5 3.5 2.8 3.2 2.9 3.1 2.99…

A: We can solve this by using definition of limit

Q: x +1 lim а—1 х2 — 1 x-

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