Questions from General Calculus

Q: Let / (a) Find an expression for g

Let (a) Find an expression for g(x) similar to the one for f (x). (b) Sketch the graphs of f and g. (c) Where is f differentiable? Where is t differentiable?

Q: The area labeled B is three times the area labeled A.

The area labeled B is three times the area labeled A. Express b in terms of a.

Q: Differentiate. f (t) = tet cot t

Differentiate. f (t) = tet cot t

Q: Explain exactly what is meant by the statement that “differentiation and

Explain exactly what is meant by the statement that “differentiation and integration are inverse processes.”

Q: Find dy/dx by implicit differentiation. ey sin x

Find dy/dx by implicit differentiation. ey sin x = x + xy

Q: Prove, using the definition of derivative, that if f

Prove, using the definition of derivative, that if f (x) = cos x, then f ‘(x) = -sin x.

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 = sin x + cos x, (0, 1)

Q: Find f ’ (x) and f ’’ (x).

Find f ’ (x) and f ’’ (x). f(x) = x2 / 1+ex

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 = ex cos x, (0, 1)

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 = cos x - sin x, (π, -1)