Questions from General Calculus

Q: Differentiate the function. f (x) = log2 (

Differentiate the function. f (x) = log2 (1 – 3x)

Q: Differentiate the function. f (x) = log5 (

Differentiate the function. f (x) = log5 (xex)

Q: Graphs of the velocity functions of two particles are shown, where

Graphs of the velocity functions of two particles are shown, where is measured in seconds. When is each particle speeding up? When is it slowing down? Explain.

Q: Let f (x) = x/√1 – cos 2x

Let f (x) = x/√1 – cos 2x (a). Graph f. What type of discontinuity does it appear to have at 0? (b). Calculate the left and right limits of f at 0. Do these values confirm your answer to part (a)?

Q: The position function of a particle is given by s = t3

The position function of a particle is given by s = t3 – 4.5t2 – 7t, t > 0. (a). When does the particle reach a velocity of 5 m/s? (b). When is the acceleration 0? What is the significance of this val...

Q: If a ball is given a push so that it has an

If a ball is given a push so that it has an initial velocity of 5 m/s down a certain inclined plane, then the distance it has rolled after seconds is s = 5t + 3t2. (a). Find the velocity after 2 s. (b...

Q: If a stone is thrown vertically upward from the surface of the

If a stone is thrown vertically upward from the surface of the moon with a velocity of 10 m/s, its height (in meters) after seconds is h = 10t – 0.83t2. (a). What is the velocity of the stone after 3...

Q: (a). The cubic function f (x) = x

(a). The cubic function f (x) = x (x – 2) (x – 6) has three distinct zeros: 0, 2, and 6. Graph f and its tangent lines at the average of each pair of zeros. What do you notice? (b). Suppose the cubic...

Q: (a). Use the identity for tan (x – y

(a). Use the identity for tan (x – y) (see Equation 14b in Appendix C) to show that if two lines L1 and L2 intersect at an angle a, then tan a = m2 – m1/1 + m1m2 wh...

Q: A car is traveling at night along a highway shaped like a

A car is traveling at night along a highway shaped like a parabola with its vertex at the origin. The car starts at a point 100 m west and 100 m north of the origin and travels in an easterly directio...