Questions from General Calculus

Q: Show that the function defined by the upper branch of the hyperbola

Show that the function defined by the upper branch of the hyperbola y2/a2 - x2/b2 = 1 is concave upward.

Q: Find an equation for the ellipse with foci (1, 1

Find an equation for the ellipse with foci (1, 1) and (21, 21) and major axis of length 4.

Q: Determine the type of curve represented by the equation /

Determine the type of curve represented by the equation in each of the following cases: (d) Show that all the curves in parts (a) and (b) have the same foci, no matter what the value of k is.

Q: (a) Show that the equation of the tangent line to

(a) Show that the equation of the tangent line to the parabola y2 = 4px at the point (x0, y0) can be written as (b) What is the x-intercept of this tangent line? Use this fact to draw the tangent line...

Q: Test the series for convergence or divergence. /

Test the series for convergence or divergence.

Q: Show that the tangent lines to the parabola x2 = 4py drawn

Show that the tangent lines to the parabola x2 = 4py drawn from any point on the directrix are perpendicular.

Q: Show that if an ellipse and a hyperbola have the same foci

Show that if an ellipse and a hyperbola have the same foci, then their tangent lines at each point of intersection are perpendicular.

Q: Use parametric equations and Simpson’s Rule with n = 8 to estimate

Use parametric equations and Simpson’s Rule with n = 8 to estimate the circumference of the ellipse /

Q: The dwarf planet Pluto travels in an elliptical orbit around the sun

The dwarf planet Pluto travels in an elliptical orbit around the sun (at one focus). The length of the major axis is 1.18 × 1010 km and the length of the minor axis is 1.14 × 1010 km. Use Simpson’s Ru...

Q: Find the area of the region enclosed by the hyperbola x2/

Find the area of the region enclosed by the hyperbola x2/a2 - y2/b2 = 1 and the vertical line through a focus.