Questions from General Calculus

Q: Find the derivative of the function. y = cos √

Find the derivative of the function. y = cos √sin (tan πx)

Q: A particle moves according to a law of motion s = f

A particle moves according to a law of motion s = f (t), t > 0, where is measured in seconds and in feet. (a). Find the velocity at time t. (b). What is the velocity after 3 s? (c). When is the partic...

Q: Zoom in toward the points (1, 0), (0

Zoom in toward the points (1, 0), (0, 1), and (-1, 0) on the graph of the function g (x) = (x2 – 1)2/3. What do you notice? Account for what you see in terms of the differentiability of g.

Q: Find the derivative of the function. y = 23x2

Find the derivative of the function. y = 23x2

Q: Find y' and y". y = cos (x2)

Find y' and y". y = cos (x2)

Q: Find y' and y". y = cos2x

Find y' and y". y = cos2x

Q: Find y' and y". y = eax sin βx

Find y' and y". y = eax sin βx

Q: Find dy/dx by implicit differentiation. 2√x

Find dy/dx by implicit differentiation. 2√x + √y = 3

Q: Show by implicit differentiation that the tangent to the ellipse x2/

Show by implicit differentiation that the tangent to the ellipse x2/a2 + y2/b2 = 1 at the point (x0, y0) is x0x/a2 + y0y/b2 = 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 = (1 + 2x)10, (0, 1)