Questions from General Calculus

Q: Sketch the set of all points (x, y) such

Sketch the set of all points (x, y) such that |x + y | ≤ ex.

Q: If P(a, a2) is any point on the

If P(a, a2) is any point on the parabola y = x2, except for the origin, let Q be the point where the normal line at P intersects the parabola again (see the figure). (a) Show that the y-coordinate of...

Q: If a ball is thrown vertically upward with a velocity of 80

If a ball is thrown vertically upward with a velocity of 80 ft/s, then its height after t seconds is s = 80t - 16t2. (a) What is the maximum height reached by the ball? (b) What is the velocity of the...

Q: For what values of c does the curve y = cx3 +

For what values of c does the curve y = cx3 + ex have inflection points?

Q: An isosceles triangle is circumscribed about the unit circle so that the

An isosceles triangle is circumscribed about the unit circle so that the equal sides meet at the point s0, ad on the y-axis (see the figure). Find the value of a that minimizes the lengths of the equa...

Q: Sketch the region in the plane consisting of all points (x

Sketch the region in the plane consisting of all points (x, y) such that 2xy ≤ |x - y | ≤ x2 + y2

Q: Use a computer with three-dimensional graphing software to graph the

Use a computer with three-dimensional graphing software to graph the surface. Experiment with viewpoints and with domains for the variables until you get a good view of the surface. -4x2 - y2 + z2 = 1...

Q: The line y = mx + b intersects the parabola y =

The line y = mx + b intersects the parabola y = x2 in points A and B. (See the figure.) Find the point P on the arc AOB of the parabola that maximizes the area of the triangle PAB.

Q: ABCD is a square piece of paper with sides of length 1

ABCD is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from B to D with center A. The piece of paper is folded along EF, with E on AB and F on AD, so that A falls on the q...

Q: For which positive numbers a does the curve y = ax intersect

For which positive numbers a does the curve y = ax intersect the line y = x?