Problem 37
Approximate \(\lim _{x \rightarrow 5} \frac{x^{2}+2 x-35}{x^{2}-10.5 x+27.5}\)
Problem 37
Find the equations of the tangent and normal lines to the graph of \(g\) at the indicated point. \(g(s)=e^{s}\left(s^{2}+2\right)\) at (0,2).
Problem 37
Use logarithmic differentiation to find \(\frac{d y}{d x}\), then find the equation of the tangent line at the indicated \(x\) -value. $$y=(1+x)^{1 / x}, \quad x=1$$
Problem 38
Use logarithmic differentiation to find \(\frac{d y}{d x}\), then find the equation of the tangent line at the indicated \(x\) -value. $$y=(2 x)^{x^{2}}, \quad x=1$$
Problem 38
Find the equations of the tangent and normal lines to the graph of \(g\) at the indicated point. \(g(t)=t \sin t\) at \(\left(\frac{3 \pi}{2},-\frac{3 \pi}{2}\right)\).
Problem 38
Use the Bisection Method to approximate, accurate to two decimal places, the root of \(g(x)=x^{3}+x^{2}+x-1\) on [0.5,0.6].
Problem 39
Find the equations of the tangent and normal lines to the graph of \(g\) at the indicated point. \(g(x)=\frac{x^{2}}{x-1}\) at (2,4).
Problem 39
Give intervals on which each of the following functions are continuous. (a) \(\frac{1}{e^{x}+1}\) (b) \(\frac{1}{x^{2}-1}\) (c) \(\sqrt{5-x}\) (d) \(\sqrt{5-x^{2}}\)
Problem 39
Use logarithmic differentiation to find \(\frac{d y}{d x}\), then find the equation of the tangent line at the indicated \(x\) -value. $$y=\frac{x^{x}}{x+1}, \quad x=1$$
Problem 39
Given that \(e^{o}=1\), approximate the value of \(e^{0.1}\) using the tangent line to \(f(x)=e^{x}\) at \(x=0\).
