91Ó°ÊÓ

Solve the given problems. Find the slope of a line tangent to the curve of \(y=x / \tan ^{-1} x\) at \(x=0.80 .\) Verify the result by using the numerical derivative feature of a calculator.

Solve the given problems.Display the graphs of \(y_{1}=\sec ^{2} x\) and \(y_{n}=[\tan (x+h)-\tan x] / h\) on the same screen of a calculator for \(-\pi / 2

Solve the given problems. (a) Display the graph of \(y=\ln x\) on a calculator, and using the derivative feature, evaluate \(d y / d x\) for \(x=2 .\) (b) Display the graph of \(y=1 / x,\) and evaluate \(y\) for \(x=2 .\) (c) Compare the values in parts (a) and (b).

Solve the given problems. Display the graphs of \(y_{1}=\sec ^{2} x\) and \(y_{n}=[\tan (x+h)-\tan x] / h\) on the same screen of a calculator for \(-\pi / 2

(a) Display the graph of \(y=\ln x\) on a calculator, and using the derivative feature, evaluate \(d y / d x\) for \(x=2 .\) (b) Display the graph of \(y=1 / x,\) and evaluate \(y\) for \(x=2 .\) (c) Compare the values in parts (a) and (b).

Solve the given problems by finding the appropriate derivative. A package of weather instruments is propelled into the air to an altitude of about \(7 \mathrm{km} .\) A parachute then opens, and the package returns to the surface. The altitude \(y\) of the package as a function of the time \(t\) (in min) is given by \(y=\frac{10 t}{e^{0.4 t}+1} .\) Find the vertical velocity of the package for \(t=8.0\) min.

Solve the given problems. Find the linearization of the function \(f(x)=\frac{6 e^{4 x}}{2 x+3}\) for \(a=0\)

Find the linearization of the function \(f(x)=\frac{6 e^{4 x}}{2 x+3}\) for \(a=0\).

Solve the given problems. On a calculator, find the values of (a) \(-\sin 1.0000\) and (b) \((\cos 1.0001-\cos 1.0000) / 0.0001 .\) Compare the values and give the meaning of each in relation to the derivative of the cosine function where \(x=1\)

Solve the given problems. Find the second derivative of \(y=x \tan ^{-1} x\)