Number 
Question 
Answer 
See the work 
1.

Find the equation for the line tangent to the parametric curve:
at the points where t= 3 and t= 3. For t= 3, the tangent line (in form y = mx+b) is y=_______. For t= 3 , the tangent line is y= ______.

see the work
see the work

The work
Point Cost: 2 
2.

(a) Find expressed as a function of t for the given the parametric equations:
___.
(b) Find expressed as a function of t. ___________

see the work

The work
Point Cost: 3 
3.

Consider the parametric curve:
At which t value(s) is the tangent to this curve vertical? t=_______. Write the point(s) at which the tangent is vertical. ________
At which t value(s) is the tangent to this curve horizontal? t= ______ Write the point(s) at which the tangent is horizontal. ________

t= 0
tangent is vertical at (4, 0)
t= 1.732, 1.732
tangent to the horizontal:
(1, 10.392), (1, 10.392)

The work
Point Cost: 3 
4.

Use a graph to estimate the coordinates of the highest point and the leftmost point on the curve
Then find the exact coordinates. Highest point:______. Leftmost point:_____. The curve has one horizontal asymptote and one vertical asymptote. Find them. Horizontal asymptote: y= ______. Vertical asymptote: x= _______.

Highest point: (13.59, 2.575) Leftmost point: (1.839, 19.028) y= 0 x= 0 
The work
Point Cost: 3 
5.

Find the equation of the tangent line to the curve x=5t^4+1 y=4t^5+1 that passes through the point (6, 5). Write the answer in the form y= mx+b. y=_______

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The work
Point Cost: 2 
6.

Use the parametric equations of an ellipse
to find the area that it encloses.

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The work
Point Cost: 3 
7.

Find the area bounded by the curve x=t1/t y=t+1/t and the line y= 17/4 Area=______

10.39 
The work
Point Cost: 5 
8.

Find the length of the curve
.

4935.747

The work
Point Cost: 3 
9.

Consider the parametric equation
What is the length of the curve for
to

1.31081 
The work
Point Cost: 3 
10.

Find the equation for the line tangent to the parametric curve:
at the points where t=5 and t=5.
For t=5, the tangent line (in form y=mx+b) is
y=________
For t=5 , the tangent line is
y=________

see number 1

The work 