Questions from General Calculus

Q: Investigate the family of curves given by the equation f (x

Investigate the family of curves given by the equation f (x) = x4 + cx2 + x. Start by determining the transitional value of at which the number of inflection points changes. Then graph several members...

Q: (a). Investigate the family of polynomials given by the equation

(a). Investigate the family of polynomials given by the equation f (x) = cx4 – 2x2 + 1. For what values of does the curve have minimum points? (b). Show that the minimum and maximum points of every cu...

Q: (a). Investigate the family of polynomials given by the equation

(a). Investigate the family of polynomials given by the equation f (x) = 2x3 + cx2 + 2x. For what values of does the curve have maximum and minimum points? (b). Show that the minimum and maximum point...

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...

Q: The figure shows a sector of a circle with central angle θ

The figure shows a sector of a circle with central angle θ. Let A (θ)be the area of the segment between the chord PR and the arc PR. Let B(θ) be the area of the...

Q: (a). Graph the function. (b). Use

(a). Graph the function. (b). Use l’Hospital’s Rule to explain the behavior as x→0. (c). Estimate the minimum value and intervals of concavity. Th...

Q: Investigate the family of curves given by f (x) =

Investigate the family of curves given by f (x) = xe-cx, where c is a real number. Start by computing the limits as x→±∞. Identify any transitional values of where the basic shape changes. What happen...

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...

Q: For what values of and is the following equation true? lim

For what values of and is the following equation true? lim x→0 (sin 2x/x3 + a + b/x2)

Q: If f' is continuous, use l’Hospital’s Rule to show that Explain

If f' is continuous, use l’Hospital’s Rule to show that Explain the meaning of this equation with the aid of a diagram.