W12 Stepwise

Due date: Friday 4/3, 11:59pm

Parametric curves

01

01

Convert parametric curve to function graph

Write the following curves as the graphs of functions $y=f(x)$. (Find $f(x)$ for each case.)

(a) $x=t+3$, $y=4t$ and $0<t<1$

(b) $x=\cos t$, $y={\sin }^{2}t$ and $0<t<2\pi$

Sketch each curve.

Link to original

Solution

Transclude of calculus-ii/homeworks/w12/solutions---0265-01

Parametric calculus

02

01

Parametric curves: Points with given slope

Where on the image of $(3t^2-2t,t^3-6t)$ does the tangent line have slope $3$?

Link to original

Solution

Transclude of calculus-ii/homeworks/w12/solutions---0260-01

03

02

Parametric concavity

Find $\frac{d^{2}y}{d{x}^2}$ at $t=1$ for the curve given parametrically by $x=4-t^{-2}$, $y=t^{-1}+t$.

Link to original

Solution

Transclude of calculus-ii/homeworks/w12/solutions---0260-02