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.
Certified Tutor
All Calculus 2 Resources
