Questions from General Calculus

Q: Find an equation of the hyperbola with foci (0, ±

Find an equation of the hyperbola with foci (0, ±4) and asymptotes y = ±3x.

Q: Find an equation for the ellipse that shares a vertex and a

Find an equation for the ellipse that shares a vertex and a focus with the parabola x2 + y = 100 and that has its other focus at the origin.

Q: Find the curve that passes through the point (3, 2

Find the curve that passes through the point (3, 2) and has the property that if the tangent line is drawn at any point P on the curve, then the part of the tangent line that lies in the first quadran...

Q: Use the method of cylindrical shells to find the volume generated by

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves about the given axis.

Q: Show that if m is any real number, then there are

Show that if m is any real number, then there are exactly two lines of slope m that are tangent to the ellipse x2/a2 + y2/b2 = 1 and their equations are

Q: Use the Table of Integrals on the Reference Pages to evaluate the

Use the Table of Integrals on the Reference Pages to evaluate the integral.

Q: Find the values of x for which the series converges. Find

Find the values of x for which the series converges. Find the sum of the series for those values of x.

Q: Show that the angles between the polar axis and the asymptotes of

Show that the angles between the polar axis and the asymptotes of the hyperbola / are given by /

Q: Evaluate the integral. /

Evaluate the integral.

Q: A curve called the folium of Descartes is defined by the parametric

A curve called the folium of Descartes is defined by the parametric equations (a) Show that if (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line...