Questions from General Calculus

Q: Simplify the expression. tan (sin-1 x)

Simplify the expression. tan (sin-1 x)

Q: Simplify the expression. sin (tan-1 x)

Simplify the expression. sin (tan-1 x)

Q: Simplify the expression. cos (2 tan-1 x

Simplify the expression. cos (2 tan-1 x)

Q: Graph the given functions on the same screen. How are these

Graph the given functions on the same screen. How are these graphs related?

Q: The figure shows graphs of f, f', f'' and f'''

The figure shows graphs of f, f', f'' and f'''. Identify each curve, and explain your choices.

Q: Graph the given functions on the same screen. How are these

Graph the given functions on the same screen. How are these graphs related?

Q: Prove Formula 2 by the same method as for Formula 1.

Prove Formula 2 by the same method as for Formula 1.

Q: (a). Prove that sin-1 x = π/

(a). Prove that sin-1 x = π/2. (b). Use part (a) to prove Formula 2. sin1x cos1x

Q: Find the derivative of the function. Simplify where possible.

Find the derivative of the function. Simplify where possible. y = (tan-1 x)2

Q: Find the derivative of the function. Simplify where possible.

Find the derivative of the function. Simplify where possible. y = tan-1 (x2)