Area A piece of wire 20 centimeters long is cut at a point x centimeters from the left end, as shown in the following diagram. The left-hand piece is formed into a circle and the righthand piece is formed into a square. a. Find the area enclosed by the two figures as a function of x. b. Complete the following table. Round the area to the nearest hundredth. c. What is the domain of this function? 20 x2 x Total Area Enclosed (cm2)048121620
Lecture 30 Antiderivatives (Section 4.9) ex. Suppose that the slope of the tangent line of a function f(x)atny x-value is given by 2x − 5. Can we find f(x) Def. Af unin F is called an of f on an interval I if for all x in I. ex. Find an antiderivative of the function f(x)= x + x. How many antiderivatives can there be Recall the theorem (page L24 - 8) which states that if two functions have the same derivative on an interval, they can only differ by a constant. Theorem: If F is an antiderivative of f on I,ten is the most general antiderivative of f on hew C represents any constant.
