Questions from General Calculus

Q: In Example 4 we considered a member of the family of functions

In Example 4 we considered a member of the family of functions f (x) = sin (x + sin cs) that occur in FM synthesis. Here we investigate the function with c = 3. Start by graphing f in the viewing rect...

Q: Use a graph to estimate the coordinates of the leftmost point on

Use a graph to estimate the coordinates of the leftmost point on the curve x = t4 – t2, y = t + ln t. Then use calculus to find the exact coordinates.

Q: Graph the curve in a viewing rectangle that displays all the important

Graph the curve in a viewing rectangle that displays all the important aspects of the curve. At what points does the curve have vertical or horizontal tangents?

Q: Graph the curve in a viewing rectangle that displays all the important

Graph the curve in a viewing rectangle that displays all the important aspects of the curve. At what points does the curve have vertical or horizontal tangents?

Q: Investigate the family of curves given by the parametric equations x=

Investigate the family of curves given by the parametric equations x= t3 - ct, y =t2. In particular, determine the values of for which there is a loop and find the point where the curve intersects its...

Q: The family of functions f (t) = C (e

The family of functions f (t) = C (e-at – e-bt), where a, b, and C are positive numbers and b > a, has been used to model the concentration of a drug injected into the bloodstream at time t = 0. Graph...

Q: Describe how the graph of f varies as varies. Graph several

Describe how the graph of f varies as varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points and i...

Q: Describe how the graph of f varies as varies. Graph several

Describe how the graph of f varies as varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points and i...

Q: Describe how the graph of f varies as varies. Graph several

Describe how the graph of f varies as varies. Graph several members of the family to illustrate the trends that you discover. In particular, you should investigate how maximum and minimum points and i...

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f' and f" to estimate the intervals of increase and decrease, extreme values, intervals...