\def\frac#1#2{{{#1}\over{#2}}}
\def\textfrac#1#2{{{\textstyle#1}\over{\textstyle#2}}}
\def\scriptfrac#1#2{{{\scriptstyle#1}\over{\scriptstyle#2}}}
\def\s{\hskip 3em}
\def\m{\hskip 1em}
\def\d{\displaystyle}

\def\dd#1{{\mathsurround=0pt$#1$}}

\def\high#1{^{^{\hbox to 0pt{$\scriptstyle#1$\hss}}}}
\long\def\hide#1\endhide{}

\let\xlim=\lim
\def\lim_#1{\xlim_{#1}\>}
\def\pt(#1,#2){\hbox{\mathsurround=0pt$\left(#1,#2\right)$}}
\def\nms#1{{\mathsurround=0pt{#1}}}
\everyproblem={\mathsurround=4pt}
\normalafterproblemskip=1cm
%\input examI.perm
\title{Math 105 Test I}
\date{Sept. 17, 1991}
%%\lastversion=2

\problem %** 1 **%
The domain of $f(x) = \frac{{x^3-1}}{(x+2)(x^2+3)}$ is

\correct $x\neq -2$
\wrong $x\neq -2, x\neq\pm\sqrt 3$
\wrong $x\neq 1,  2, \pm\sqrt3$
\wrong $|x|\geq 3$
\wrong  $x\neq -3$

\problem %** 2 **%
If $f(x) =(x^2+x+1)\sqrt{x^2-4}$ then its value at $x=1$ is
\correct undefined
\wrong$3^{3/2}$
\wrong$-3^{3/2}$
\wrong$3\sqrt2$ 
\wrong$-3\sqrt2$


\problem %** 3 **%
If $f(x)=x^3+x^2+1$ then $f(1)+f(2)$ is equal to
\correct $16$
\wrong$17$
\wrong$18$
\wrong$19$
\wrong$20$



\problem %** 4 **%
If $f(x) = x^2+1$ and $g(x) =x-2$ then $f\bigl(g(x)\bigr)$ is given by
\correct $x^2-4x+5$
\wrong$x^2-1$
\wrong$x^2+1$
\wrong$(x^2+1)(x-2)$
\wrong$x^2-x$



\problem %** 5 **%
The curves $y=x^2-2x$ and $y=-x+2$ meet at the point(s)
\correct\pt(-1,3) and \pt(2,0)
\wrong\pt(1,1) and (-2,4)
\wrong\pt(-1,2)
\wrong\pt(-2,1)
\wrong there are no points of intersection



\problem %** 6 **%
The quadratic $4x^2+4x-8$ can be factored as
\correct$4(x-1)(x+2)$
\wrong$4(x+1)(x-2)$
\wrong$4(x+4)(x-2)$
\wrong$4(x-1)(x-2)$
\wrong$4(x+1)(x+2)$



\problem %** 7 **%
The expression $\bigl[(x^2+2x+1)^{-3}\bigr]\hskip -4pt\high{1/6}$\qquad
is the same as
\wrong$x^2+2x+1$
\wrong$\frac1{2x+1}$
\correct$\frac 1{\sqrt{x^2+2x+1}}$
\wrong$x^2+x+1$
\wrong$(x+1)^{3/2}$


\problem %** 8 **%
The slope of the line joining \pt(1,2) and \pt(3,5) is
\correct$\frac32$
\wrong$\frac23$
\wrong$-\frac32$
\wrong$-\frac23$
\wrong$\frac53$


\problem %** 9 **%
The line $4y+3x=5$ has slope 
\correct$-\frac 34$
\wrong$\frac34$
\wrong$\frac53$
\wrong$\frac54$
\wrong$-\frac43$


\problem %** 10 **%
The \dd y intercept of the line $6x+5y=30$ is
\correct\pt(0,6)
\wrong\pt(1,2)
\wrong\pt(0,5)
\wrong\pt(5,0)
\wrong\pt(6,0)


\problem %** 11 **%
Any line parallel to $3x+2y =7$ has slope
\correct $-\frac 32$
\wrong$\frac 23$
\wrong$\frac73$
\wrong$\frac72$
\wrong$-\frac 23$


\problem %** 12 **%
An equation of the line containing the points \pt(1,3) and \pt(5,7) is
\correct$y=x+2$
\wrong$y=-x+7$
\wrong$y=x-2$
\wrong$y=2x+1$
\wrong$y=-2x+1$



\problem %** 13 **%
The \dd x intercept of
the line $3y+2x-6=0$ is
\correct\pt(3,0)
\wrong\pt(2,0)\wrong\pt(0,3)
\wrong\pt(0,2)\wrong the line has no \dd x intercept
\problem %** 14 **%
An equation for the tangent line to the curve $y=x^3+x^2+x+1$ at \pt(1,4) is
\correct$y=6x-2$
\wrong$y=3x+1$
\wrong$y=4x$
\wrong$y=5x-1$
\wrong$y=7x-3$


\problem %** 15 **%
The point on the graph of $y = x^2$ where the tangent line is parallel to the line
$y+4x=3$ is
\correct\pt(-2,4)\wrong\pt(1,1)\wrong\pt(-3,9)\wrong\pt(2,4)\wrong\pt(8,64)



\problem %** 16 **%
The derivative of $\root 7 \of x$ is
\correct$\frac 1{7x\high{6/7}}$
\wrong$7x^6$
\wrong$\frac 17 x\high{6/7}$
\wrong$\frac 7{x\high{6/7}}$
\wrong none of these

\problem %** 17 **%
The limit $\displaystyle\lim_{x\to 1}\frac{x^2-9}{x-3}$ is equal to
\correct $4$
\wrong$3 $\wrong$2$\wrong$1$\wrong$0$


\problem %** 18 **%
The limit $\displaystyle\lim_{x\to 0}\frac{(x+2)^2-x^2-4}{x}$ is equal to
\correct $4$
\wrong$8$
\wrong$-8$
\wrong$-4$
\wrong$0$

\problem %** 19 **%
The limit $\displaystyle\lim_{x\to\infty}\frac{2x+1}{x+2}$ is equal to
\correct $2$
\wrong $\frac 12$
\wrong$0$
\wrong$-\frac 12$
\wrong does not exist


\hide
\problem %** 20 **%
The derivative of the function $f(x)=\frac 1{\sqrt{1-x}}$ is
\correct $\frac 1{2(1-x)^{3/2}}$
\wrong $\frac 2{\sqrt{1-x}}$
\wrong $-\frac 1{2\sqrt{1-x}}$
\wrong $(1-x)^{3/2}$
\wrong $\sqrt{1-x}$
\endhide

\problem %** 21 **%
The derivative of the function $f(x)=(x^2+1)^3$ is
\correct $6x(x^2+1)^2$
\wrong  $3x(x^2+1)^2$
\wrong  $6x(x^2+1)$
\wrong  $3x(x^2+1)$
\wrong  $\frac{(x^2+1)^4}4$

\end

