Calculus AB : Limits and Continuity
Study concepts, example questions & explanations for Calculus AB
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Example Questions
Example Question #7 :Apply Intermediate Value Theorem
Can Intermediate Value Theorem be applied to the function
Yes, because the function
No, because
No, because the function is not continuous
Yes, because the function crosses the
No, because
The required conditions for Intermediate Value Theorem include the function must be continuous and
Example Question #8 :Apply Intermediate Value Theorem
What can be concluded by using Intermediate Value Theorem for the function
There is a root for this polynomial located between
The requirements for Intermediate Value Theorem are not met
There is a root for this polynomial at
There are two roots on this polynomial located between
There is a root for this polynomial located between
his function is continuous (as it is a polynomial) and
Example Question #9 :Apply Intermediate Value Theorem
Let
Yes, as shown by Intermediate Value Theorem
No, Intermediate Value Theorem cannot determine the exact value of
Yes, as shown by the Fundamental Theorem of Calculus
No, no number c such that
Yes, as shown by Intermediate Value Theorem
First, determine the values of the function at the bounds. This will allow the correct implementation of the Intermediate Value Theorem.
Because the problem asks to analyze the interval
Example Question #10 :Apply Intermediate Value Theorem
Assume
If
If
This is true because for continuous functions, Intermediate Value Theorem states that a change in sign (ex: from positive to negative) of the function within an interval suggests a root (where the function crosses the
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