a. A function is defined by f(x) = |x| , calculate f(-3), f(4), and sketch the graph.

b.

a. Find the domain and sketch the graph of the function (f(x) = x² – 6x).
b. Estimate the area between the curve y = x² and the lines y = 1 and y = 2.

a. Find the Maclaurin series for cos x and prove that it represents cos x for all x.
b. Find the volume of a sphere of radius r

Define continuity on an interval. Show that the function f(x) = 1 − √(1 − x²) is continuous on the interval [−1, 1].

Verify Mean value theorem of f(x) = x³ – 3x + 2 for [-1, 2].

Stating with x₁ = 2, find the third approximation x₃  to the root of the equation x³ – 2x – 5 = 0

Find the volume of the resulting solid which is enclosed by the curve y = x and y = x² is rotated about the x-axis.

Find the solution of y” + 4y’ + 4 = 0.

If a = (4, 0, 3) and b = (-2, 1, 5) find |a|, the vector a – b and 2a + b

Find the extreme values of the function (f(x, y) = x² + 2y²) on the circle (x² + y² = 1).