Which of the following decimal numbers are examples of terminating decimals?
2 answers:
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The value of n given the form of the function is (b) positive odd number
<h3>How to interpret the graph?</h3>The form of the graph is given as:
f(x) = a(x + k)^1/n + c
For the given graph, we have the following features:
a > 0 --- a is positive
k > 0 --- k is positive
c < 0 --- c is negative
If n is an even number, the function would be undefined because the even root of a number is undefined
However, the function is defined if n is an odd number,
Hence, the value of n given the form of the function is a positive odd number
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Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
Then, an antiderivative of this is:
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and
Since this this function is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means: