%\magnification 1200
          \def\marknumbers#1{}
\marknumbers{1,20}
\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}   %%%equivalent to \dsize in ams.tex
\def\pt(#1,#2){\hbox{\mathsurround=0pt$\left(#1,#2\right)$}}
\def\nms#1{{\mathsurround=0pt{#1}}}
\everyproblem={\mathsurround=4pt}
\normalafterproblemskip=1.5cm
\multiplechoiceskip=10pt

\pageannouncements={none}
%\marknumbers{1,20}
%\twocolumn{16}
%\twocolumn{p.5}
%\def\section{{\bf Class Time:}}

\def\HonorCodeStatement{ 
\hbox{I have not violated the Honor Code in any way with regard to this
work.}\hskip -4in 
\lower .8cm \hbox{Signature: \vrule height .2pt depth 0pt width 3.74in} 
}
\answersheetfootline{\HonorCodeStatement}

\input exam.perm1
\def\st{\perm1:abcde \perm2:edcba}
\title{Math 105{--}Test I}
\date{Feb.\ 1, 1994}
\lastversion=2


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

\correct  $x>3$
\wrong  $x\geq 0, \; x\neq 1$
\wrong  $x\neq 3, \; x\neq -1, \; x\neq 1$
\wrong $x<3, \;  x\neq -1 ,\; x \neq 1$
\wrong $x\geq 0$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 2 **%
The equation for the line through the point \pt(2,3) and parallel to 
$x-y=1$ is 

\correct $x-y=-1$
\wrong $x+y=5$
\wrong $y = x +4$
\wrong $y = 3x +2 $
\wrong $y = 3x -2 $

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 3 **%
If $f(x) = x^2+1$ and $g(x)=\sqrt{x-3}$, then

\correct $g(f(x))=\sqrt{x^2-2}$
\wrong $g(f(x))=x-2$
\wrong $g(f(x))= (x^2+1)\sqrt{x-3}$
\wrong $g(f(x))= x^2+1+\sqrt{x-3}$
\wrong $g(f(x))= x^2+x-2$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 4 **%
The expression $x^2 - 7x -18$ can be factorized as

\correct $(x-9)(x+2)$
\wrong $(x+9)(x-2)$
\wrong $(x-3)(x+6)$
\wrong $(x+3)(x-6)$
\wrong $(x+3)(x+6)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 5 **%
If $f(x) = x^3 + \frac{8}{x^2}$, then $f'(2)=$

\correct $10$
\wrong $12$
\wrong $-2$
\wrong $\frac1{3}$
\wrong does not exist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 6 **%
If $f(x) = \frac{1}{\sqrt{x^3}}$,  then $f'(x)=$

\correct $-\; \frac3{2\sqrt{x^5}}$
\wrong$-\; \frac3{2{x^2}}$
\wrong$\frac3{2{x^2}}$
\wrong$\frac3{4\sqrt{x^5}}$
\wrong$-\; \frac3{4\sqrt{x}}$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 7 **%
The curves $y=x^2 + 4 $ and $y=-3x+4$ meet at the point(s)

\correct\pt(0,4) and \pt(-3,13)
\wrong \pt(-1,5) and \pt(1,5)
\wrong \pt(-\;\frac43,0) and \pt(-2, 0)
\wrong \pt(3,1)
\wrong there are no points of intersection

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 8 **%
Find the equation of the tangent line to the graph $y = 2\sqrt{x} + 5$
at a point whose y coordinate is $y= 7$. 

\correct$y =  x + 6$
\wrong$y = \frac{5}2 x + \frac{9}2$
\wrong$y = \frac{5}2 x + 7$
\wrong$y = -\; \frac{5}2 x + 7 $
\wrong$y = -\; \frac{5}2 x + \frac{19}2$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 9 **%
The expression $\bigl[(2x^2+2x+7)^{-2}\bigr]^{1/8}\sqrt{2x^2+2x+7}$ is the 
same as

\correct$\bigl[2x^2+2x+7\bigr]^{1/4}$
\wrong$\frac1{\bigl[2x^2+2x+7\bigr]^{1/4}}$
\wrong$\frac1 {\sqrt{2x^2+2x+7}}$
\wrong$\sqrt{2x^2+2x+7} $
\wrong$(2x+\sqrt7)^{1/2}$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 10 **%
$\d \lim_{x\rightarrow 2}\frac{x^2 + x - 6}{ x^2 -4}$ is equal to

\correct $\frac54$
\wrong $- \frac32$
\wrong does not exist
\wrong $1$
\wrong  $0$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 11 **%
$\d \lim_{x\rightarrow \infty}\frac{5x^5 + 4x^4 + 3x^3 +2x^2 + x +8}{ 
 6x^5- 5 x^4 - 4 x^3 - 3 x^2 - 2x + 9}$ is equal to

\correct $\frac56$
\wrong $\frac89$
\wrong $-\; \frac45$
\wrong $-\; \frac34$
\wrong does not exist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 12 **%
$\d \lim_{x\rightarrow 4}\frac{\sqrt{x} - 2}{ x -4}$ is equal to

\correct $\frac14$
\wrong $\frac12$
\wrong $-\;\frac14$
\wrong $-\; \frac12$
\wrong does not exist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 13 **%
If $f(x)= x^{99} - x^{98}$, then $\d \lim_{h\rightarrow 0}
\frac{f(1+h) - f(1) }{ h}$ is equal to

\correct $1$
\wrong $99$
\wrong $-98$
\wrong $\frac{(1+h)^{99}-(1+h)^{98}}h$
\wrong does not exist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 14 **%
If $f(x) = \sqrt{x^{88} + 9}$, then $f'(x)=$

\correct $\frac{44 x^{87}}{\sqrt{x^{88} + 9}}$
\wrong $\frac{88 x^{87}}{\sqrt{x^{88} + 9}}$
\wrong ${88 x^{87}}{\sqrt{x^{88} + 9}}$
\wrong ${(88 x^{87}+9)}{\sqrt{x^{88} + 9}}$
\wrong does not exist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% \problem %** 15 **%
%% Suppose that $f(x)$ and $g(x)$ are differentiable and $f(1) = 8$, $g(1) = 8$,
%% $f(8) = -1$, $g(8) = -2$, $f'(1) = 2$, $g'(1)=3$, $f'(8)=4$ and $g'(8)=5$.
%% If $h(x)=g(f(x))$, then $h'(1)=$
%% 
%% \wrong 12
%% \wrong 6
%% \wrong 20
%% \wrong $ -8$
%% \correct 10

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 15 **%
If $f(x)=(3x^4  -1 )^2$, then $f'(x)=$

\wrong $2(3x^4-1)$
\wrong $12x^3$
\correct $24x^3(3x^4-1)$
\wrong $12x^3(3x^4-1)$
\wrong $ 72 x^7$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 16 **%
$\d \lim_{x\rightarrow 1} \frac{ 3x^2 + 7x+2}{2x^2 + 3x -3}=$

\correct $6$
\wrong $\frac32$
\wrong $-\;\frac23$
\wrong $\frac73$
\wrong does not exist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 17 **%
Which equation of the following is perpendicular to the equation
$ x + 2y = 0$, and passes through the point \pt(1,7)? 

\correct $ y = 2x +5$
\wrong $ x- 2y = -13$
\wrong $ y = -\frac12 x +\frac{15}2$
\wrong $ y = \frac12 x + \frac{13}2$
\wrong $y= - 2x + 9$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 18 **%

An equation for the tangent line to the curve
$y = x^3 - 5x + 3$ at the point \pt(2,1) is

\correct$y=7x-13$
\wrong$y=2x - 3$
\wrong$y= 3x-7$
\wrong$y=\frac x3 + 3$
\wrong$y=5x-3$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 19 **%
The $y$-intercept of the line $4x+5y+6=0$ is

\wrong \pt(-\;\frac32,0)
\wrong \pt(\frac32,0)
\wrong \pt(0, \frac65)
\correct \pt(0,-\;\frac65)
\wrong \pt(1,2)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\problem %** 20 **%

How many real solutions does the equation $x^2 - 4x + 5 =0$ have?

\correct 0
\wrong  1
\wrong  2
\wrong  3
\wrong  4

\end


