Questions from General Calculus

Q: The figure shows a circle with radius 1 inscribed in the parabola

The figure shows a circle with radius 1 inscribed in the parabola y = x2. Find the center of the circle.

Q: Find the point where the curves y = x3 – 3x +

Find the point where the curves y = x3 – 3x + 4 and y = 3 (x2 – x) are tangent to each other, that is, have a common tangent line. Illustrate by sketching both curves and the common tangent.

Q: Show that the tangent lines to the parabola y = ax2 +

Show that the tangent lines to the parabola y = ax2 + bx + c at any two points with x-coordinates p and q must intersect at a point whose -coordinate is halfway between p and q.

Q: The figure shows a point P on the parabola and the point

The figure shows a point P on the parabola and the point Q where the perpendicular bisector of OP intersects the y-axis. As P approaches the origin along the parabola, what happens to Q? Does it have...

Q: The graphs of a function f and its derivative f' are shown

The graphs of a function f and its derivative f' are shown. Which is bigger, f' (-1) or f"(1)?

Q: A tangent line is drawn to the hyperbola xy = c at

A tangent line is drawn to the hyperbola xy = c at a point P. (a). Show that the midpoint of the line segment cut from this tangent line by the coordinate axes is P. (b). Show that the triangle formed...

Q: Evaluate limx→0 |2x -1|- |2x +

Evaluate limx→0 |2x -1|- |2x + 1|/x

Q: Sketch the region in the plane defined by each of the following

Sketch the region in the plane defined by each of the following equations.

Q: The figure shows a rotating wheel with radius 40 cm and a

The figure shows a rotating wheel with radius 40 cm and a connecting rod AP with length 1.2 m. The pin P slides back and forth along the -axis as the wheel rotates counter clockwise at a rate of 360 r...

Q: A fixed point of a function f is a number c in

A fixed point of a function f is a number c in its domain such that f (c) = c. (The function doesn’t move c; it stays fixed.) (a). Sketch the graph of a continuous function with domain [0, 1] whose ra...