Questions from General Calculus

Q: Differentiate. f (x) = xex csc x

Differentiate. f (x) = xex csc x

Q: Differentiate. y = x2 sin x tan x

Differentiate. y = x2 sin x tan x

Q: Prove that d/dx (csc x) = -csc

Prove that d/dx (csc x) = -csc x cot x.

Q: Prove that d/dx (sec x) = sec x

Prove that d/dx (sec x) = sec x tan x.

Q: Prove that d/dx (cot x) = -csc2x

Prove that d/dx (cot x) = -csc2x.

Q: The table gives the population of the world in the 20th century

The table gives the population of the world in the 20th century. (a). Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines. (b). Use a graphing calc...

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

Prove, using the definition of derivative, that if f (x) = csc 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 = sec x, (π/3, 2)

Q: Differentiate. y = 2csc x + 5 cos x

Differentiate. y = 2csc x + 5 cos 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 = ex cox, (0, 1)