What is your number?
2 answers:
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Answer:
(a) 0
(b) f(x) = g(x)
(c) See below.
Step-by-step explanation:
Given rational function:
<u>Part (a)</u>
Factor the <u>numerator</u> and <u>denominator</u> of the given rational function:
Substitute x = -1 to find the limit:
Therefore:
<u>Part (b)</u>
From part (a), we can see that the simplified function f(x) is the same as the given function g(x). Therefore, f(x) = g(x).
<u>Part (c)</u>
As x = 1 is approached from the right side of 1, the numerator of the function is positive and approaches 2 whilst the denominator of the function is positive and gets smaller and smaller (approaching zero). Therefore, the quotient approaches infinity.