"If 2x≤g(x)≤x4−x2+2 for all x, evaluate limx tends..." was answered by our experts

embelurildmixjm

Open question

2022-08-19

If

2 x \leq g (x) \leq x^{4} - x^{2} + 2

for all x, evaluate

lim x

tends to 1 g(x).

Answer & Explanation

kostikvento84

Beginner2022-08-20Added 4 answers

2 x \leq g (x) \leq x^{4} - x^{2} + 2

When x=1:
bottom function: 2x=2(1)=2
top function:

x^{4} - x^{2} + 2 = 1^{4} - 1^{2} + 2 = 2

Since it is given that g(x) is between the two functions then g(x) must also approach 2 by the Squeeze Theorem.

lim_{x \Rightarrow 1} g (x) = 2

Result:
2

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