91Ó°ÊÓ

Find the derivative of the function. Simplify where possible. \(y=x \sin ^{-1} x+\sqrt{1-x^{2}}\)

\(1-38=\) 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. $$\lim _{x \rightarrow 1^{+}} \ln x \tan (\pi x / 2)$$

Differentiate the function. $$ F(t)=e^{t \sin 2 t} $$

Find the derivative. Simplify where possible. $$ f(x)=x \sinh x-\cosh x $$

Find an explicit formula for \(f^{-1}\) and use it to graph \(f^{-1}, f,\) and the line \(y=x\) on the same screen. To check your work, see whether the graphs of \(f\) and \(f^{-1}\) are reflections about the line. $$ f(x)=x^{4}+1, \quad x \geqslant 0 $$

Find the limit. $$\lim _{x \rightarrow 2^{-}} e^{3 /(2-x)}$$

Find the derivative. Simplify where possible. possible. $$ g(x)=\cosh (\ln x) $$

Find an explicit formula for \(f^{-1}\) and use it to graph \(f^{-1}, f,\) and the line \(y=x\) on the same screen. To check your work, see whether the graphs of \(f\) and \(f^{-1}\) are reflections about the line. $$ f(x)=2-e^{x} $$

\(1-38=\) 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. $$\lim _{x \rightarrow \infty} x \tan (1 / x)$$

Find the derivative of the function. Simplify where possible. \(y=\arctan \sqrt{\frac{1-x}{1+x}}\)