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 November 3rd, 2018, 08:34 AM #1 Newbie   Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0 Hi I need to answer the following equation: $\displaystyle \lim_{x\to2}$ (x³ + 3x - 1) = x3 = x to the power of 3 Last edited by skipjack; November 3rd, 2018 at 11:37 AM.
 November 3rd, 2018, 10:51 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,251 Thanks: 516 Show x to the power of 3 as x^3. One way to answer this question is to use the laws of limits. $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) + g(x) \implies \lim_{x \rightarrow a} h(x) = b + c.$ $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) - g(x) \implies \lim_{x \rightarrow a} h(x) = b - c.$ $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) * g(x) \implies \lim_{x \rightarrow a} h(x) = bc.$ $\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \ c \ne 0, \text { and } h(x) = \dfrac{f(x)}{g(x)} \implies \lim_{x \rightarrow a} h(x) = \dfrac{b}{c}.$ Thanks from topsquark
 November 3rd, 2018, 11:06 AM #3 Newbie   Joined: Sep 2018 From: Spain Posts: 11 Thanks: 0 Okay, so what's the answer? Last edited by skipjack; November 3rd, 2018 at 11:39 AM.
 November 3rd, 2018, 11:38 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,101 Thanks: 1905 What do you get by replacing each "x" in "x³ + 3x - 1" with "2" and evaluating the result?
November 3rd, 2018, 12:50 PM   #5
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 Originally Posted by raven2k7 Okay, so what's the answer?
The answer is that it's time for you to do some work for yourself.

 November 3rd, 2018, 01:59 PM #6 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,637 Thanks: 119 Informally, substitute x = 2 Formally, limit of a sum is sum of its summands limits, and limit of a product is product of its factors limits. limit x = 2.
November 3rd, 2018, 02:32 PM   #7
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 Originally Posted by raven2k7 Okay, so what's the answer?
lmao

November 4th, 2018, 03:23 AM   #8
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 Originally Posted by zylo Informally, substitute x = 2 Formally, limit of a sum is sum of its summands limits, and limit of a product is product of its factors limits. limit x = 2.
by the way, none of those results were correct. lol

November 4th, 2018, 03:57 AM   #9
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 Originally Posted by raven2k7 by the way, none of those results were correct. lol

 November 4th, 2018, 05:35 AM #10 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra He is clearly clever enough that he doesn't need any help.

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