,
we can still find 
!Calculus
Lesson
60
More
Parametrics
Back to Dr. Nandor's Calculus Notes Page
Back to Dr. Nandor's Calculus Page
Even if we can't find ,
we can still find !
Example: 
Check: 
How would we find 
?
From previous example: 
We can convert this to a function of x if we want to or check
with 
.
More examples:
Find the slope and concavity at 
of
Find the slope and concavity at 
of
If Arc Length and Surface Area were Covered:
Examples: Circle:
Epicycloid:
How much tape in a roll, where the tape is 0.001 in thick, the
hole is 1/2 in, the outer radius is 2 in?
Use 
after squaring and simplifying, use integral table to integrate 
Answer: 11,781 in or 982 feet
Similarly, 