Projectile motion The range R of a projectile fired from the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity at an angle with the horizontal, then in Chapter 12 we find that where g is the downward acceleration due to gravity. Find the angle ? for which the range R is the largest possible.

Math 1225 x2.3 Limit Laws Lect 1 Rules to ▯gure out limits of functions Theorem: Basic Limit Rules ▯ Basic limits: Let k be a and a be Then lim k = lim x = x!a x!a ▯ Properties: Assume that lim f(x) = and lim g(x) = x!a x!a And that c is a .Then 1. x!a[f(x) + g(x)] = 2. lim[cf(x)] = x!a Note: x!a [f(x) ▯ g(x)] = 3. lim [f(x)g(x)] = x!a f(x) 4. x!a g(x) = whenever M ▯ What kind of limits can we compute using the above ▯ 2 ▯ Example 1: lim ▯5x + 1 = x!4