Let ( 4 x leq g(x)+3 x leq x^{4}-x^{2}+4 ) for all ( x ). Then ( lim _{x ightarrow 1} g(x)= )
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We can subtract \(3x\) from all parts of the inequality to get: \(4x - 3x \leq g(x) + 3x - 3x \leq x^4 - x^2 + 4 - 3x\). Simplifying further, we have: \(x \leq g(x) \leq x^4 - x^2 + 4 - 3x\). Now, let's consider the limit as \(x\) approaches 1. Taking the limit Show more…
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