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Calc 2 9.2

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

 

 

 

Find the equation for the line tangent to the
parametric curve:
x=t^3-9t y=9t^2-t^4
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 dy/dx expressed as a function of t for the given
the parametric equations:

x=7t+lnt y=4t-lnt
dy/dx= ___.

(b) Find d^2y/dx^2 expressed as a function of t.
d^2y/dx^2=___________

 

dy/dx= (4*t-1)/(7t+1)
d^2y/dx^2= see the work
The work

Point Cost: 3

3.

 

 

 

 

 

 

Consider the parametric curve:

x=4-t^2 y=t^3-9t

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

x= 5te^t,         y= 7te^-t

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=_______

 

see work
The work

Point Cost: 2

6.

 

 

 

Use the parametric equations of an ellipse
x= 11cosø
y= 8sinø
0≤ø≤2π
to find the area that it encloses.

 

see work
The work

Point Cost: 3

7.

 

 

 

Find the area bounded by the curve
x=t-1/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
x= 1+21t^2, y= 3+14t^3, 0≤t≤7.

 

4935.747

 

The work

Point Cost: 3

9.

 

 

Consider the parametric equation
x= 17(cos(theta)+(theta)sin(theta))
y= 17(sin(theta);-(theta)cos(theta))
What is the length of the curve for theta= 0 to theta= (1/8)π

 

1.31081
The work

Point Cost: 3

10.

 

 

Find the equation for the line tangent to the parametric curve:
x=t^3-25t
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