Questions from General Calculus

Q: Use the Comparison Theorem to determine whether the integral is convergent or

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

Q: Find the area of the region bounded by the hyperbola y2 -

Find the area of the region bounded by the hyperbola y2 - x2 = 1 and the line y = 3.

Q: Determine whether the series is convergent or divergent. If it is

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

Q: (a) Use the reduction formula in Example 6 to show

(a) Use the reduction formula in Example 6 to show that where n > 2 is an integer. (b) Use part (a) to evaluate (c) Use part (a) to show that, for odd powers of sine,

Q: Determine whether the series is convergent or divergent. /

Determine whether the series is convergent or divergent.

Q: Find the area of the region bounded by the curves /

Find the area of the region bounded by the curves

Q: Use series to approximate the definite integral to within the indicated accuracy

Use series to approximate the definite integral to within the indicated accuracy.

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

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

Q: We can extend our definition of average value of a continuous function

We can extend our definition of average value of a continuous function to an infinite interval by defining the average value off on the interval / (a) Find the average value of y = tan-1 x on the inte...

Q: Use the substitution u = 1/x to show that

Use the substitution u = 1/x to show that