Precalculus : Introductory Calculus
Study concepts, example questions & explanations for Precalculus
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Example Questions
Example Question #41 : Introductory Calculus
Find the following limit:
To solve, simply realize you are dealing with a limit whose numerator and demominator have the same max power. Thus the limit is simply the division of their coefficient.
Example Question #1 : Determine If A Function Is Continuous Using Limits
Find the domain where the following function is continuous:
The function in the numerator factors to:
so if we cancel the x+3 in the numerator and denominator we have the same function but it is continuous. The 
Example Question #1 : Determine If A Function Is Continuous Using Limits
What are the discontinuities in the following function and what are their types?
Since the factor 
Since the factor
There is no discontinuity at all at 
Example Question #662 : Pre Calculus
Determine if the function 
No, it is not continuous because the lefthand and righthand limits do not equal the value of the function at 0.
Yes, it is continuous because the lefthand and righthand limits are equal.
Yes, it is continuous because the righthand and lefthand limits are equal to the actual value of the function.
No, it is not continuous because the lefthand limit does not match the righthand limit.
Yes, it is continuous because the righthand and lefthand limits are equal to the actual value of the function.
In order to determine if a function is continuous at a point three things must happen.
1) Taking the limit from the lefthand side of the function towards a specific point exists.
2) Taking the limit from the righthand side of the function towards a specific point exists.
3) The limits from 1) and 2) are equal and equal the value of the original function at the specific point in question.
In our case,
1)
2) 
3)
Because all of these conditions are met, the function is continuous at 0.
Example Question #1 : Determine If A Function Is Continuous Using Limits
Determine if 
No, it is not continuous because the lefthand and righthand limits do not equal the value of the function at 0.
No, it is not continuous because the lefthand limit does not match the righthand limit.
Yes, it is continuous because the lefthand and righthand limits are equal.
Yes, it is continuous because the righthand and lefthand limits are equal to the actual values of the function.
Yes, it is continuous because the righthand and lefthand limits are equal to the actual values of the function.
First, find that at any point where 
Then find that
As these are all equal, it can be determined that the function is continuous on all points of its domain.
Example Question #5 : Determine If A Function Is Continuous Using Limits
Let 
As 
The 
Therefore, our function is continuous at all values of 
Example Question #1 : Rate Of Change Problems
Find the average rate of change of the function 
The average rate of change will be found by 
Here, 
Now, we have 
Example Question #2 : Rate Of Change Problems
Let a function be defined by 
Find the average rate of change of the function over 
We use the average rate of change formula, which gives us 
Now 
Therefore, the answer becomes 
Example Question #2 : Derivatives
Suppose we can model the profit, 
Find the average rate of change of the profit from 
We need to apply the formula for the average rate of change to our profit equation. Thus we find the average rate of change is 
Since 
Example Question #3 : Derivatives
Let the profit, 
Find the average rate of change in profit when production increases from 4 items to 5 items.
Since 
Therefore the average rate of change formula gives us 
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