All High School Math Resources
Example Questions
Example Question #1 :Using Limits With Continuity
The above graph depicts a function. Doesexist, and why or why not?
exists because
does not exist because
exists because
does not exist because
does not exist because.
does not exist because.
exists if and only if. As can be seen from the diagram,, but. Since,does not exist.
Example Question #1 :Calculus Ii — Integrals
The above graph depicts a function. Doesexist, and why or why not?
does not exist because
exists because
does not exist becauseis not continuaous at.
does not exist because
does not exist because
exists because
exists if and only if;
the actual value ofis irrelevant, as is whetheris continuous there.
As can be seen,
and;
therefore,,
andexists.
Example Question #2 :Using Limits With Continuity
A function is defined by the following piecewise equation:
At, the function is:
continuous
discontinuous
continuous
The first step to determine continuity at a point is to determine if the function is defined at that point. When we substitute in 3 for, we get 18 as our-value.is thus defined for this function.
The next step is determine if the limit of the function is defined at that point. This means that the left-hand limit must be equal to the right-hand limit at. Substitution reveals the following:
Both sides of the function, therefore, approach a-value of 18.
Finally, we must ensure that the curve is smooth by checking the limit of the derivative of both sides.
Since the function passes all three tests, it is continuous.
Example Question #1 :Limits
The graph depicts a function. Doesexist?
does not exist because.
does not exist becauseis undefined.
does not exist becauseis not continuous at.
exists becauseis constant on.
exists because.
exists because.
exists if and only if; the actual value ofis irrelevant.
As can be seen,and; therefore,, andexists.
Example Question #1 :Understanding Polar Coordinates
The polar coordinates of a point are. Give its-coordinate in the rectangular coordinate system (nearest hundredth).
Given the polar coordinates, the-coordinate is. We can find this coordinate by substituting:
Example Question #1 :Calculus Ii — Integrals
The polar coordinates of a point are. Give its-coordinate in the rectangular coordinate system (nearest hundredth).
Given the polar coordinates, the-coordinate is. We can find this coordinate by substituting:
Example Question #1 :Calculus Ii — Integrals
The polar coordinates of a point are. Give its-coordinate in the rectangular coordinate system (nearest hundredth).
Given the polar coordinates, the-coordinate is. We can find this coordinate by substituting:
Example Question #1 :Understanding Polar Coordinates
The polar coordinates of a point are. Give its-coordinate in the rectangular coordinate system (nearest hundredth).
Given the polar coordinates, the-coordinate is. We can find this coordinate by substituting:
Example Question #1 :Parametric, Polar, And Vector
Find the vector where its initial point isand its terminal point is.
We need to subtract the-coordinate and the当考虑到坐标求解一个向量initial and terminal coordinates:
Initial pt:
Terminal pt:
Vector:
Vector:
Example Question #1 :Understanding Vector Coordinates
Find the vector where its initial point isand its terminal point is.
We need to subtract the-coordinate and the-coordinate to solve for a vector when given its initial and terminal coordinates:
Initial pt:
Terminal pt:
Vector:
Vector:
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