All Calculus 2 Resources
Example Questions
Example Question #511 : Calculus Ii
Given the above graph of , over which of the following intervals is
continuous?
For a function to be continuous at a given point
, it must meet the following two conditions:
1.) The point must exist, and
2.) .
Examining the above graph, is continuous at every possible value of
except for ,
. Thus,
is continuous on the interval .
Example Question #511 : Limits
Given the above graph of , over which of the following intervals is
continuous?
For a function to be continuous at a given point
, it must meet the following two conditions:
1.) The point must exist, and
2.) .
Examining the above graph, is continuous at every possible value of
except for , . Thus,
is continuous on the interval .
Example Question #12 : Limits And Continuity
Given the above graph of , over which of the following intervals is
continuous?
For a function to be continuous at a given point
, it must meet the following two conditions:
1.) The point must exist, and
2.) .
Examining the above graph, is continuous at every possible value of
except for . Thus,
is continuous on the interval .
Example Question #1 : Parametric Form
Rewrite as a Cartesian equation:
So
or
We are restricting
to values on , so is nonnegative; we choose.
Also,
So
or
We are restricting
to values on , so is nonpositive; we choose
or equivalently,
to make
nonpositive.
Then,
and
Example Question #1 : Parametric, Polar, And Vector
Write in Cartesian form:
Rewrite
using the double-angle formula:
Then
which is the correct choice.
Example Question #1 : Parametric
Write in Cartesian form:
, so
.
, so
Example Question #3 : Parametric, Polar, And Vector
Write in Cartesian form:
,
so the Cartesian equation is
.
Example Question #4 : Parametric, Polar, And Vector
Write in Cartesian form:
so
Therefore the Cartesian equation is
.Example Question #2 : Functions, Graphs, And Limits
Rewrite as a Cartesian equation:
, so
This makes the Cartesian equation
.
Example Question #2 : Parametric, Polar, And Vector
and . What is in terms of (rectangular form)?
In order to solve this, we must isolate
in both equations.and
.
Now we can set the right side of those two equations equal to each other since they both equal
..
By multiplying both sides by
, we get , which is our equation in rectangular form.All Calculus 2 Resources
