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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. Then use calculus to find the exact values.

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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 triangle PQR. Find lim θ→0+ A(θ)/B(θ)....

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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...

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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...

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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...

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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...

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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...

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Q: If f' is the function considered in Example 3, use a

If f' is the function considered in Example 3, use a computer algebra system to calculate f' and then graph it to confirm that all the maximum and minimum values are as given in the example. Calculate...

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Q: Sketch the graph by hand using asymptotes and intercepts, but not

Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve...

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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. Estimate the intervals of increase and decrease and intervals of concavity, and use calculus to find these intervals exactly.

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