Differential equationsIf 2x <= g(x) <= x^(4)-x^(2)+2 for all x, evaluate lim x tends to 1 g(x).
2 months ago
If 2x <= g(x) <= x^(4)-x^(2)+2 for all x, evaluate lim x tends to 1 g(x).
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Best Answer
Danishca29 Staff answered 2 months ago
2x <= g(x) <= 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 -> 1)g(x)=2 Result: 2
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