Limits

Sep 2018
19
0
Spain
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 a moderator:
May 2016
1,310
551
USA
Show x to the power of 3 as x^3.

One way to answer this question is to use the laws of limits.

$\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) + g(x) \implies \lim_{x \rightarrow a} h(x) = b + c.$

$\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) - g(x) \implies \lim_{x \rightarrow a} h(x) = b - c.$

$\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \text { and } h(x) = f(x) * g(x) \implies \lim_{x \rightarrow a} h(x) = bc.$

$\displaystyle \lim_{x \rightarrow a} f(x) = b, \ \lim_{x \rightarrow a} g(x) = c, \ c \ne 0, \text { and } h(x) = \dfrac{f(x)}{g(x)} \implies \lim_{x \rightarrow a} h(x) = \dfrac{b}{c}.$
 
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Sep 2018
19
0
Spain
Okay, so what's the answer?
 
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skipjack

Forum Staff
Dec 2006
21,481
2,470
What do you get by replacing each "x" in "x³ + 3x - 1" with "2" and evaluating the result?
 
Mar 2015
1,720
126
New Jersey
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.
 
Sep 2018
19
0
Spain
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
 

v8archie

Math Team
Dec 2013
7,712
2,682
Colombia
He is clearly clever enough that he doesn't need any help.
 
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