Given $h(2) = 4$ and $h^{\(\prime\)}(2)=-1$, use linear approximation to find the estimated value of $h(2.1)$.

Use linear approximations to estimate the value of $\sqrt{170}$. Choose an appropriate value of $a$ that minimizes the error.

A cyclist covers a distance of $2$ kilometers in a time that is $30$ seconds less than the standard time. Using the function $s\left(x\right)=\frac{7200}{120+x}$, that gives the cyclist's speed (in meters per second) as a function of $x$, where $x$ is the number of seconds more or less than the standard time for $2$ kilometers, calculate the cyclist's average speed.

Estimate the value of $(1.0009{)}^{90}$ using the approximation $(1+x{)}^k\approx 1+kx$.