How for does the projectile travel horizontally before it

Question

1. Apply the slope predictor formula to find the slope of the line tangent to y = f(x) = (2x + 4)² - (2x -4)². Then write the equation of the line tangent to the graph of f at the point (3, f(3)).

2. Find all points on the curve y = (x+4)(x-5) at which the tangent line is horizontal.

3. suppose that a projectile is fired at an angle of 45^o from the horizontal. Its initial position is the origin in the xy-plane, and its initial velocity is 100√2 ft/sec. Then its trajectory will be part of the parabola y = x - (x/25)² for which y ≥0.

(a) How for does the projectile travel (horizontally) before it hits the ground?

(b) What is the maximum height above the ground that the projectile attains?

4. Evaluate lim_x→16 (√x - 4) / (x - 16)

5. Given f(x) = 4/√(x +8), use the four-step process to find a slope predictor function m(x). Then write an equation for the line tangent to the curve at the point x = 8.

6. Use one-sided limits to find the limit or determine that the limit does not exist

lim_x→4⁺ (16 - x²) / (4 - x)

7. Find the trigonometric limit:

lim_x→0 sin 3x / 2x

8. Use the Squeeze law of limits to find the limit.

lim_x→0 x² sin 10x

9. Given h(x) = (x -9)/|x-9|, tell where h is continuous.

10. Given f(x) = (x -4) /(x² - 16), find all points where f is not defined (and therefore not continuous). For each point, tell whether or not the discontinuity is removable.

11. Given

,

Find a value for c so that f(x) is continuous for all x.

12. Determine where the function f(x) = x + [|x²|] - [|x|] is continuous.