Question 1

Find $\frac{dy}{dx}$ for the parametric equation

$x=3t^{2}$, $y=t+e^{t}$

Accepted Answer

$\frac{dy}{dx}=\frac{1+e^{t}}{6t}$

Answer

$\frac{dy}{dx}=\frac{1+e^{t}}{6t^{2}}$

Answer

$\frac{dy}{dx}=\frac{1-e^{t}}{6t}$

Answer

$\frac{dy}{dx}=\frac{1-e^{t}}{6t^{2}}$

Question 2

Find the gradient of the equation:

$x=3t^{2}$, $y=t+e^{t}$

at t=1

Accepted Answer

0.619

Answer

0.319

Answer

0.419

Answer

0.519

Question 3

Find where  the parametric equation

$x=t^{3}$, $y=1-t^{2}$

Has a gradient of 0

Accepted Answer

When $t=\frac{1}{2}$

Answer

When $t=\frac{1}{5}$

Answer

When $t=\frac{1}{4}$

Answer

When $t=\frac{1}{3}$

Question 4

Find the area under the parametric curve:

$x=3t^{2}$, $y=t-1$

In the domain $0\leq t \leq 2$

Accepted Answer

4

Answer

3

Answer

5

Answer

2

Question 5

Find the arc length of the parametric curve:

$x=3t^{2}$, $y=t^{2}$

In the domain $0\leq t \leq 2$

Accepted Answer

$8\sqrt{10}$

Answer

$6\sqrt{10}$

Answer

$7\sqrt{10}$

Answer

$5\sqrt{10}$

Question 6

Find an equation tangent to the curve of the following equation at point (1,3)

$x=1+\ln{t}$, $y=t^{2}+2$

Accepted Answer

$y=2x+1$

Answer

$y=2x-1$

Answer

$y=3x+1$

Answer

$y=3x-1$

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