Questions from General Calculus

Q: Find the derivative of the function. y = √(x

Find the derivative of the function. y = √(x+√(x+√x))

Q: Write the composite function in the form f (g (x

Write the composite function in the form f (g (x)). [Identify the inner function u = g (x) and the outer function y = f (u).] Then find the derivative dy/dx. y = sin (cot x)

Q: Find y' and y". y = eex

Find y' and y". y = eex

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 = √1 + x3, (2, 3)

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 (sin x), (π, 0)

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 + sin2x, (0, 0)

Q: (a). Find an equation of the tangent line to the

(a). Find an equation of the tangent line to the curve y = 2/ (1 + e-x) at the point (0, 1). (b). Illustrate part (a) by graphing the curve and the tangent line on the same screen.

Q: Suppose that we don’t have a formula for g (x)

Suppose that we don’t have a formula for g (x) but we know that g (2) = -4 and g'(x) = √x2 + 5 for all x. (a). Use a linear approximation to estimate g (1.95) and g (2.05). (b). Are your estimates in...

Q: (a). The curve y = |x|/√2 –

(a). The curve y = |x|/√2 – x2 is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (1, 1). (b). Illustrate part (a) by graphing the curve and the tangent lin...

Q: (a). If f (x) = x√2

(a). If f (x) = x√2 – x2, find f'(x). (b). Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f'.