91影视

For the following exercises, evaluate by any method. $$ \frac{d}{d x} \ln (\sec x+\tan x) $$

For the following exercises, find the derivatives tor the functions.\(\sinh ^{-1}(\cosh (x))\)

Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 0} \frac{e^{x}-1}{x} $$

In the following exercises, use a calculator to graph the antiderivative \(\int f\) with \(C=0\) over the given interval \([a, b] .\) Approximate a value of \(C\), if possible, such that adding \(C\) to the antiderivative gives the same value as the definite integral \(F(x)=\int_{a}^{x} f(t) d t\). [T] \(\int \frac{2 e^{-2 x}}{\sqrt{1-e^{-4 x}}} d x\) over \([0,2]\)

Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 0} x \sin \left(\frac{1}{x}\right) $$

In the following exercises, integrate using the indicated substitution. $$ \int \frac{y-1}{y+1} d y ; u=y+1 $$

For the following exercises, find the derivatives tor the functions.\(\cosh ^{-1}\left(x^{3}\right)\)

Use a calculator to graph the function and estimate the value of the limit, then use L'H么pital's rule to find the limit directly. $$ \lim _{x \rightarrow 1} \frac{x-1}{1-\cos (\pi x)} $$

[T] Find the arc length of \(\ln x\) from \(x=1\) to \(x=2\).

In the following exercises, integrate using the indicated substitution. $$ \int \frac{1-x^{2}}{3 x-x^{3}} d x ; u=3 x-x^{3} $$