Questions from General Calculus

Q: Find all points of intersection of the given curves. r

Find all points of intersection of the given curves. r = sin θ, r = 2θ

Q: Find all points of intersection of the given curves. r2

Find all points of intersection of the given curves. r2 = sin 2θ, r2 = cos 2θ

Q: Sketch the curve with the given polar equation. r =

Sketch the curve with the given polar equation. r = 2 cos 4θ

Q: Use a graph to estimate the values of θ for which the

Use a graph to estimate the values of θ for which the curves r = 3 + sin 5θ and r = 6 sin θ intersect. Then estimate the area that lies inside both curves.

Q: Find the exact length of the polar curve. r =

Find the exact length of the polar curve. r = 3 sin θ, o < θ < π/3

Q: Find the exact length of the polar curve. r =

Find the exact length of the polar curve. r = e2θ, o < θ < 2π

Q: Sketch the curve and find the area that it encloses.

Sketch the curve and find the area that it encloses. r = 2 – sin θ

Q: Find the exact length of the polar curve. r =

Find the exact length of the polar curve. r = θ2, o < θ < 2π

Q: Find the exact length of the polar curve. r =

Find the exact length of the polar curve. r = θ, o < θ < 2π

Q: Use a calculator to find the length of the curve correct to

Use a calculator to find the length of the curve correct to four decimal places.