Answer:
18.85 inches.
Step-by-step explanation:
We have been given that the radius of a smaller circle 3 inch. We are asked to find the circumference of smaller circle.
We know that circumference of a circle is equal to , where r represents radius of circle.
Therefore, the circumference of smaller circle is approximately 18.85 inches.
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: