Questions from General Calculus

Q: Suppose f (π/3) = 4 and f'(

Suppose f (π/3) = 4 and f'(π/3) = -2, and let g (x) = f (x) sin x and h (x) = (cos x)/f (x). Find (a). g'(π/3) (b). h'(π/3)

Q: (a). Use the definition of derivative to calculate f'.

(a). Use the definition of derivative to calculate f'. (b). Check to see that your answer is reasonable by comparing the graphs of f and f'. f (x) = x4 + 2x

Q: For what values of does the graph of have a horizontal tangent

For what values of does the graph of have a horizontal tangent? f (x) = ex cos x

Q: Let f (x) = x – 2 sin x,

Let f (x) = x – 2 sin x, 0 < x < 2π. On what interval is f increasing?

Q: (a). The curve y = x/ (1 +

(a). The curve y = x/ (1 + x2) is called a serpentine. Find an equation of the tangent line to this curve at the point (3,0.3). (b). Illustrate part (a) by graphing the curve and the tangent line on t...

Q: A mass on a spring vibrates horizontally on a smooth level surface

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x (t) = 8 sin t, where is in seconds and in centimeters. (a). Find the velocity and acc...

Q: (a). If f (x) = ex/ (

(a). If f (x) = ex/ (2x2 + x + 1), find f'(x). (b). Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f'.

Q: The edge of a cube was found to be 30 cm with

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing (a)...

Q: A ladder 10 ft long rests against a vertical wall. Let

A ladder 10 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let be the distance from the bottom of the ladder to the wall. If the bottom of the...

Q: (a). If f (x) = (x2 –

(a). If f (x) = (x2 – 1) ex, find f'(x) and f"(x). (b). Check to see that your answers to part (a) are reasonable by comparing the graphs of f, f', and f".