Questions from General Calculus

Q: Find the exact value of each expression. cos (tan

Find the exact value of each expression. cos (tan-1 2 + tan-13)

Q: Prove that cos (sin-1 x) = √1

Prove that cos (sin-1 x) = √1 – x2.

Q: Differentiate the function. F (y) = y ln

Differentiate the function. F (y) = y ln (1 + ey)

Q: Differentiate the function. y = ln |2 – x

Differentiate the function. y = ln |2 – x = 5x2|

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

Differentiate the function. y = ln (e-x + xe-x)

Q: Differentiate the function. y = [ln (1 +

Differentiate the function. y = [ln (1 + ex)]2

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

Find y' and y". y = ln x/x2

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

Differentiate f and find the domain of f. f (x) = ln ln ln 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 = ln (x3 – 7), (2, 0)

Q: Estimate the value of f'(a) by zooming in on

Estimate the value of f'(a) by zooming in on the graph off. Then differentiate f to find the exact value of f'(a) and compare with your estimate. f (x) = 3x2 - x3, a = 1