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Calculus 1: midterm 2

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Midterm exam 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 $3\sin (-.02)$.

See next Calculus 1: midterm 2 solutions.