Questions from General Calculus

Q: Evaluate the Riemann sum for f (x) = x -

Evaluate the Riemann sum for f (x) = x - 1, -6 ≤ x ≤ 4, with five subintervals, taking the sample points to be right endpoints. Explain, with the aid of a diagram, what the Riemann sum represents.

Q: If f (x) = cos x 0 ≤ x

If f (x) = cos x 0 ≤ x ≤ 3π/4 evaluate the Riemann sum with n = 6, taking the sample points to be left endpoints. (Give your answer correct to six decimal places.) What does the Riemann sum represent...

Q: If f (x) = x2 - 4, 0 ≤

If f (x) = x2 - 4, 0 ≤ x ≤ 3, find the Riemann sum with n = 6, taking the sample points to be midpoints. What does the Riemann sum represent? Illustrate with a diagram.

Q: (a) If $3000 is invested at 5% interest

(a) If $3000 is invested at 5% interest, find the value of the investment at the end of 5 years if the interest is compounded (i) annually, (ii) semiannually, (iii) monthly, (iv) weekly, (v) daily, an...

Q: (a) How long will it take an investment to double

(a) How long will it take an investment to double in value if the interest rate is 6% compounded continuously? (b) What is the equivalent annual interest rate?

Q: Use a graph to estimate the x-intercepts of the curve

Use a graph to estimate the x-intercepts of the curve y = 1 - 2x - 5x4. Then use this information to estimate the area of the region that lies under the curve and above the x-axis.

Q: Repeat Exercise 47 for the curve y = (x2 – 1

Repeat Exercise 47 for the curve y = (x2 – 1)-1 - x4. Exercise 47: Use a graph to estimate the x-intercepts of the curve y = 1 - 2x - 5x4. Then use this information to estimate the area of the region...

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. y = x + tan x, (π , π)

Q: The velocity function (in meters per second) is given for

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) the distance traveled by the particle during the given time interval. v(t) =...

Q: The velocity function (in meters per second) is given for

The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) the distance traveled by the particle during the given time interval. v(t) =...