Reference no: EM131021407
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 45o 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 limx→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
limx→4+ (16 - x2) / (4 - x)
7. Find the trigonometric limit:
limx→0 sin 3x / 2x
8. Use the Squeeze law of limits to find the limit.
limx→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.
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