++ Prep

00:00 5 marks

Consider the function \(f(x)= \sqrt{x^2+1}\). Using asymptotic expansion techniques for large values of \(x\),

(a) Express \(f(x)\) in an equivalent form that highlights its behavior as \(x \to \infty\).

(b) Differentiate your asymptotic form to find \(f'(x)\) and determine the slope of the tangent line as \(x \to \infty\).

Hint Hint

Hint

Rewrite \(\sqrt{x^2+1}\) as \(x\sqrt{1+\frac{1}{x^2}}\) and use the binomial expansion for \(\sqrt{1+\frac{1}{x^2}}\).

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Common Errors Common Errors

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Formula Booklet

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