Questions from General Calculus

Q: Determine the infinite limit. /

Determine the infinite limit.

Q: Determine whether f’(0) exists. /

Determine whether f’(0) exists.

Q: a. Graph the function f(x) = sin x

a. Graph the function f(x) = sin x – 1/1000 sin(1000x) in the viewing rectangle [-2, 2] by [-4, 4]. What slope does the graph appear to have at the origin? b. Zoom in to the viewing window [-0.4,...

Q: A curve has equation y = f(x). a

A curve has equation y = f(x). a. Write an expression for the slope of the secant line through the points P(3, f)3)) and Q(x, f(x)). b. Write an expression for the slope of the tangent line at P.

Q: Graph the curve y = ex in the viewing rectangles [-1

Graph the curve y = ex in the viewing rectangles [-1, 1] by [0, 2], [-0.5, 0.5] by [0.5, 1.5], and [-0.1, 0.1] by [0.9, 1.1]. What do you notice about the curve as you zoom in toward the point (0, 1)?...

Q: a. Find the slope of the tangent line to the parabola

a. Find the slope of the tangent line to the parabola y = 4x - x2 at the point (1, 3) i. using Definition 1 ii. using Equation 2 b. Find an equation of the tangent line in part (a). c. Graph the p...

Q: a. Find the slope of the tangent line to the curve

a. Find the slope of the tangent line to the curve y = x - x3 at the point (1, 0) i. using Definition 1 ii. using Equation 2 b. Find an equation of the tangent line in part (a). c. Graph the curve...

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 = 4x - 3x2, (2, -4)

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 = x3 - 3x + 1, (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 = √x , (1, 1)