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{\bf\underline{MATH 111. TEST I}}
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{\bf NAME:}

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Directions: To receive full credit you must show all your work. No notes, books, etc are to be used for the test. Calculators are only allowed to be used in performing simple operations (you are not allowed to use their graphic and programing functions, m
emory, etc). 

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1.(15 points) Find $f(0)$, $f(1)$ and $f(2)$ for the function $f$ given below
\[  f(x)=\left\{ \begin{array}{ll}
            \frac{1}{x+1} &  \mbox{ if $-1<x<1$}, \\ \\
            x^2-x-1 & \mbox{ if $1\leq x$}. 
                \end{array}
   \right. \]

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2.(10 points) Let $f(x)=x^2+x+2$, $g(x)=2x+1$. Find $f(g(x))$ and write it in a simple form.

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3.(15 points) Find the points of intersection of the curves $y=x^2-3x+5$ and $y=2x+1$.

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4.(10 points) Find the equation of the line passing through the points (1,1) and (3,7).

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5.(10 points) Find the equation of the line passing through the point (1,3) and parallel to the line $y-2x=10$.

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6.(15 points) Compute the derivatives of the following functions:

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(5 points) $f(x)=3x^4-2x^2+1$ ,\hspace{5mm}$f'(x)=$

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(5 points) $g(x)=\sqrt{x^5}$ ,\hspace{5mm}$g'(x)=$

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(5 points) $h(x)=(x^2+x+1)^3$ ,\hspace{5mm}$h'(x)=$

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7.(10 points) Find the equation of the tangent line to the graph of the function $f(x)=x^3$ at the point where $x=2$.

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8.(15 points) Compute the following limits:

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$${\rm (5\;points)}\;\;\lim_{x\rightarrow1}\;(x^3+3x^2+1)=\hspace{4in}\;$$

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$${\rm (5\;points)}\;\;\lim_{x\rightarrow2}\;\frac{x^2+2}{2x-1}=\hspace{4in}\;$$

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$${\rm (5\;points)}\;\;\lim_{x\rightarrow2}\;\frac{x^2-3x+2}{x-2}=\hspace{4in}\;$$


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