Chapter 3: Q24E (page 150)
To determine the value of \(\mathop {\lim }\limits_{x \to \infty } \left( {{e^{ - {x^2}}}} \right)\).
The value of \(\mathop {\lim }\limits_{x \to \infty } \left( {{e^{ - {x^2}}}} \right)\) is 0
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Prove the identity \(coshx - sinhx = {e^{ - x}}\).
(a) Determine the value of \({f^{ - 1}}(17)\) if\(f\) is one-to-one and \(f(6) = 17\).
(b) Determine the value of \(f(2)\) if\(f\) is one-to-one and \({f^{ - 1}}(3) = 2\).
Prove the identity\({(\cosh x + \sinh x)^n} = \cosh nx + \sinh nx\) where n is any real number.
1–38 ■ Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.
3.\(\mathop {lim}\limits_{x \to {{\left( {\frac{\pi }{2}} \right)}^ + }} \frac{{cosx}}{{1 - sinx}}\).
To determine the value of \(\mathop {\lim }\limits_{x \to \infty } \left( {{e^{ - 2x}}\cos x} \right)\)
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