$1.(i)$ should read "A sequence $[...]is$ always monotone." For $1e$ you may assume that the function $f(x)is$ defined $in$ such a way that $itis$ possible $to$ compute those surface areas. $Itis$ not meant $tobe$ a trick question.

For the questions that ask about positive numbers: zero $is$ not considered a positive number, $tobe$ clear

Mark $as$ true $or$ false

$(a)(2$ points$)$ True

False

$(b)(2$ points$)$ True

False

$(c)(2$ points$)$ True

False

${\displaystyle \underset{\frac{1}{2}}{\overset{1}{}}}\frac{\sqrt[\phantom{2}]{81x^8-9x^4+1}}{3x}dx={\displaystyle \underset{1}{\overset{2}{}}}-\frac{\sqrt[\phantom{2}]{81-9t^4+t^8}}{3t^5}dt$

$(d)(2$ points$)$ True

False

For any function $f(x)$ defined $on$ the whole real line, the parame$-$

terization $x(t)=lnt,y(t)=f(lnt),t>0$ gives the same curve $as$

$y=f(x)$

$(e)(2$ points$)$ True

False

The areas $of$ the surfaces formed $by$ the curves $y=f(x)$ and $y=$

$a-f(x)$ over $0xb$ rotated around the $y-$axis are equal for

any real number a and every function $f(x)$

$(f)(2$ points$)$ True

False

The surface area $of$ a solid with finite volume $is$ always finite

$(g)(2$ points$)$ True

False

$r=$acos$+$bsin$is$ the equation $ofan$ ellipse $in$ polar coordinates

$(h)(2$ points$)$ True

False

The series

${\displaystyle \underset{n=}{\overset{}{}}}$

${?}_k{e}^{-kn}$

converges for any fixed positive integer $k$

$(i)(2$ points$)$ True

False

A sequence $of$ formed $by$ Riemann sums $ofan$ increasing continuous

function $on$ a finite interval $a,bn=$ the number

$of$ subintervals $$