Questions from General Calculus


Q: (a) Prove the reduction formula / (b

(a) Prove the reduction formula (b) Use part (a) to evaluate (c) Use parts (a) and (b) to evaluate

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Q: Test the series for convergence or divergence. /

Test the series for convergence or divergence.

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Q: Estimate the errors involved in Exercise 63, parts (a)

Estimate the errors involved in Exercise 63, parts (a) and (b). How large should n be in each case to guarantee an error of less than 0.00001? Data from Exercise 63: (a) the Trapezoidal Rule, (b) th...

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Q: If a surveyor measures differences in elevation when making plans for a

If a surveyor measures differences in elevation when making plans for a highway across a desert, corrections must be made for the curvature of the earth. (a) If R is the radius of the earth and L is t...

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Q: Evaluate the indefinite integral as an infinite series. /

Evaluate the indefinite integral as an infinite series.

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Q: Evaluate the integral. /

Evaluate the integral.

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Q: The speedometer reading (v) on a car was observed at

The speedometer reading (v) on a car was observed at 1-minute intervals and recorded in the chart. Use Simpson’s Rule to estimate the distance traveled by the car.

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Q: A population of honeybees increased at a rate of r(t

A population of honeybees increased at a rate of r(t) bees per week, where the graph of r is as shown. Use Simpson’s Rule with six subintervals to estimate the increase in the bee po...

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Q: Suppose you are asked to estimate the volume of a football.

Suppose you are asked to estimate the volume of a football. You measure and find that a football is 28 cm long. You use a piece of string and measure the circumference at its widest point to be 53 cm....

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Q: Determine whether the sequence converges or diverges. If it converges,

Determine whether the sequence converges or diverges. If it converges, find the limit.

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