Questions from General Calculus

Q: Find a formula for a function that satisfies the following conditions:

Find a formula for a function that satisfies the following conditions:

Q: Find a formula for a function that has vertical asymptotes x =

Find a formula for a function that has vertical asymptotes x = 1 and x = 3 and horizontal asymptote y = 1.

Q: The figure shows a fixed circle C1 with equation (x -

The figure shows a fixed circle C1 with equation (x -1)2 + y2 = 1 and a shrinking circle C2 with radius r and center the origin. P is the point (0, r), Q is the upper point of intersection of the two...

Q: If and are positive numbers, prove that the equation a/

If and are positive numbers, prove that the equation a/x3 + 2x2 – 1 + b/x3 + x – 2 = 0 has at least one solution in the interval (-1, 1).

Q: A cardiac monitor is used to measure the heart rate of a

A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent l...

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. y = √x, (1, 1)

Q: The point P (0, 5, 0) lies on

The point P (0, 5, 0) lies on the curve y = cos πx. (a). If Q is the point (x, cos πx), use your calculator to find the slope of the secant line (correct to six decimal places) for the following value...

Q: If a ball is thrown into the air with a velocity of

If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet seconds later is given by y = 40t – 16t2. (a). Find the average velocity for the time period beginning when t = 2 and la...

Q: The table shows the position of a cyclist. /

The table shows the position of a cyclist. (a). Find the average velocity for each time period: (i). [1, 3] (ii). [2, 3] (iii). [3, 5] (iv). [3, 4] (b) Use the graph of as a function of to estimat...

Q: The displacement (in centimeters) of a particle moving back and

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 3 cos πt, where is measured in seconds. (a). Find the aver...