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# Calculus 1: test 2

This is a set of sample tests for Calculus 1: course.

1. Calculate the derivative of $$ f(x)=x^{e}+e^{x}+x+e.$$

2. Differentiate $$g(t)=\sqrt{x} \cos x.$$

3. Evaluate $\frac{dy}{dx}$ for $$y=\sqrt{e^{x}}.$$

4. Evaluate $\frac{dy}{dx}$ for $$xy= \cos y+x.$$

5. Suppose the altitude, in m, of an object is given by the function $$y=t²+t,t≥0,$$ where $t$ is time, in sec. What is the velocity when the altitude is $12$ meters?

6. The population of a city declines by 10% every year. How long will it take to drop to 50% of the current population?

7. The area of a circle is increasing at a rate of $5$ cm²/sec. At what rate is the radius of the circle increasing when the area is $2$ cm?

8. Find the linear approximation of $f(x)=3\sin(x)$ at $a=0$. Use it to estimate $3\sin(-.02)$.