Questions from General Calculus

Q: Let / a. Evaluate each limit,

Let a. Evaluate each limit, if it exists. b. Where is f discontinuous? c. Sketch the graph of f.

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

a. Graph the function f(x) = ex + ln|x - 4| for 0 ≤ x ≤ 5. Do you think the graph is an accurate representation off ? b. How would you get a graph that represents f better?

Q: Let / a. For each of the

Let a. For each of the numbers 2, 3, and 4, discover whether g is continuous from the left, continuous from the right, or continuous at the number. b. Sketch the graph of g.

Q: Show that the function is continuous on its domain. State the

Show that the function is continuous on its domain. State the domain. h(x) = xesinx

Q: Show that the function is continuous on its domain. State the

Show that the function is continuous on its domain. State the domain. g(x) = x2 – 9 /x2 - 2

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. x5 - x3 + 3x - 5 = 0, (1, 2)

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. cos√x = ex - 2, (0, 1)

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

a. Find the slope of the tangent line to the curve y = 9 - 2x2 at the point (2, 1). b. Find an equation of this tangent line.

Q: Find equations of the tangent lines to the curve y =

Find equations of the tangent lines to the curve y = 2/ 1 - 3x at the points with x-coordinates 0 and -1.

Q: The displacement (in meters) of an object moving in a

The displacement (in meters) of an object moving in a straight line is given by s = 1 + 2t + 1/4t2, where t is measured in seconds. a. Find the average velocity over each time period. i. [1, 3] ii...