Questions from General Calculus

Q: (a). Use implicit differentiation to find y' if x2 +

(a). Use implicit differentiation to find y' if x2 + xy + y2 + 1 = 0. (b). Plot the curve in part (a). What do you see? Prove that what you see is correct. (c). In view of part (b), what can you say a...

Q: A stone is dropped into a lake, creating a circular ripple

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after (a) 1 s, (b) 3 s, and (c) 5...

Q: A spherical balloon is being inflated. Find the rate of increase

A spherical balloon is being inflated. Find the rate of increase of the surface area (S = π4r2) with respect to the radius when is (a) 1 ft, (b) 2 ft, and (c) 3 ft. What conclusion can you make?

Q: The mass of the part of a metal rod that lies between

The mass of the part of a metal rod that lies between its left end and a point meters to the right is 3x2 kg. Find the linear density (see Example 2) when is (a) 1 m, (b) 2 m, and (c) 3 m. Where is th...

Q: Differentiate the function. y = 2x log10√x

Differentiate the function. y = 2x log10√x

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

Differentiate the function. f (x) = x ln x - x

Q: Differentiate the function. y = log2 (e-x

Differentiate the function. y = log2 (e-x cos πx)

Q: Find y' and y". y = x2 ln (2x

Find y' and y". y = x2 ln (2x)

Q: Differentiate f and find the domain of f. f (

Differentiate f and find the domain of f. f (x) = x/1 – ln (x – 1)

Q: The number of yeast cells in a laboratory culture increases rapidly initially

The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function where is measured in hours. At time t = 0 the populat...