Test Section10FunctionNotationTest

Find the following value: if $4x-3(y^2+x^2y y') + 4y' = 0$, find $y'$ for $x=1$, $y=2$.

(Enter your answer as a number without any functions like sine, ln, etc.)

Evaluate mentally (without using a calculator): ${1\over2}x^{-1/2}$ at $x=1$.

(Enter your answer as a number without any functions like sine, ln, etc.)

Find the following value: if $x^2+y^2=z^2$, find $y$ for $x=3$, $z=5$, $y>0$.

(Enter your answer as a number without any functions like sine, ln, etc.)

Let $v(t)=t^2-2t$, where $v(t)$ is the velocity in ft/s of an object at time $t$. When for $t>0$ is the object stopped (when is $v(t) = 0$)?
$t =$
(Enter your answer as a number with units, leaving a space between your numerical answer and the units.)

Let $g(x) = 2(x+1)^2-4$. If $g(x) = 4$, what is the largest possible value of $x$?
$x =$

Let $g(z)=\ln(z)$. Find $g(e^2)$
$g(e^2) =$
(Simplify your answer, so that it is written without any functions like sine, ln, etc.)

Evaluate mentally (without using a calculator): $(x^2+1)(x-1)+(2x+1)\over(x+1)^2$ at $x=1$.

(Enter your answer as a number without any functions like sine, ln, etc.)

Let $f(x)=\sqrt{x^2+16}-5$. For what $x>0$ is $f(x)$ zero?
$x =$

Find the following value: if $F(x) = {1\over4}x^4 + x$, find $F(b)-F(a)$ for $a=-1$, $b=1$.

(Enter your answer as a number without any functions like sine, ln, etc.)

Evaluate mentally (without using a calculator): $-\ln x$ at $x=e$.

(Enter your answer as a number without any functions like sine, ln, etc.)