Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = ln(x), [1, 5]
1 answer:
Answer:
Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]
Step-by-step explanation:
We are given that a function
Interval [1,5]
The given function is defined on this interval.
Hypothesis of Mean Value Theorem:
(1) Function is continuous on interval [a,b]
(2)Function is defined on interval (a,b)
From the graph we can see that
The function is continuous on [1,5] and differentiable at(1,5).
Hence, the function satisfies the hypothesis of the Mean Value Theorem.
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Given:
A set of composite numbers less than 12.
To find:
The set by listing and set builder methods.
Solution:
Composite number: A positive integer is called a composite number if it has at least one divisor other than 1 and itself.
Composite numbers less than 12 are 4, 6, 8, 9, 10.
By using the listing method , the given set can be expression as:
Set = {4, 6, 8, 9, 10}
The numbers 4, 6, 8, 9, 10 are greater than 1, less than 12 and non prime numbers.
By using set builder method, the given set can be expression as:
Set =
Therefore, the list and set builder notation of the given set are {4, 6, 8, 9, 10} and respectively.