Questions from General Calculus

Q: Find the given derivative by finding the first few derivatives and observing

Find the given derivative by finding the first few derivatives and observing the pattern that occurs.

Q: Differentiate. f (x) = √x sin x

Differentiate. f (x) = √x sin x

Q: Find the given derivative by finding the first few derivatives and observing

Find the given derivative by finding the first few derivatives and observing the pattern that occurs.

Q: Suppose that f (5) = 1, f'(5

Suppose that f (5) = 1, f'(5) = 6, g (5) = -3, and g'(5) = 2. Find the following values.

Q: (a). Use the substitution θ = 5x to evaluate limx

(a). Use the substitution θ = 5x to evaluate limx→0 sin 5x/x (b). Use part (a) and the definition of a derivative to find d/dx (sin 5x)

Q: Use Formula 2 and trigonometric identities to evaluate the limit.

Use Formula 2 and trigonometric identities to evaluate the limit. limt→0 tan 6t/sin 2t

Q: Use Formula 2 and trigonometric identities to evaluate the limit.

Use Formula 2 and trigonometric identities to evaluate the limit. limx→0 sin 3x sin 5x/ x2

Q: Use Formula 2 and trigonometric identities to evaluate the limit.

Use Formula 2 and trigonometric identities to evaluate the limit. limθ→0 sin θ/θ + tan θ

Q: The frequency of vibrations of a vibrating violin string is given by

The frequency of vibrations of a vibrating violin string is given by where L is the length of the string, T is its tension, and is its linear density. [See Chapter 11 in D. E. Hall, Musical Acoustics,...

Q: Let P (x) = F (x) G (

Let P (x) = F (x) G (x) and Q (x) = F (x)/ G (x), where F and G are the functions whose graphs are shown. (a). Find p'(2). (b). Find Q'(7).