Calculus Answers

Find the indicated limit, if it exists.

limit of f of x as x approaches 0 where f of x equals 10 x plus 2 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0

Trace the curve y^2 = (x +1) (x −1)^2 by showing all the properties you use to trace it.

For which values of k, is the function f, defined as below, continuous at x = 2 ?
F(x) = 3-kx, 1≤ x is < 2.
(X^2/4) -3 ,x ≥ 2
Further, at which other points in [1,∞[ is f continuous, and why?

Trace the curve y^2 = (x +1) (x −1)^2 by showing all the properties you use to trace it.

For which values of k, is the function f, defined as below, continuous at x = 2 ?
F(x) = 3-kx, 1≤ x is < 2.
(X2/4) -3 ,x ≥ 2
Further, at which other points in [1,∞[ is f continuous, and why?

For which values of k, is the function f, defined as below, continuous at x = 2 ?
F(x) = 3-kx, 1 is less than equal to x is less than 2.
(X^2/4) -3 ,x is greater than equal to 2
Further, at which other points in [1,∞[ is f continuous, and why?

A scuba fiver dives directly from A to B, and then to C and then to the bottom of the sea at D she then realise that she has only 4 minutes' worth of oxygen left in her tank. She can ascend vertically at 10 cm/s AB=8cm, BC=12m and CD=16m. Can she reach the surface before her oxygen supply runs out?

For which values of k, is the function f, defined as below, continuous at x = 2 ?
F(x) = 3-kx, 1 is less than equal to x is less than 2.
(X^2/4) -3 ,x is greater than equal to 2
Further, at which other points in [1,∞[ is f continuous, and why?

Trace the curve y^2 = (x +1) (x −1)^2 by showing all the properties you use to trace it.

What is the smallest perimeter possible for a rectangle whose area is 16 inches?

At what point on the line x=4 does the line segment from (0,0) to(0,6) sibrend the greatest angle?