Math210 homework

Complete the following problems showing your work and clearly communicating your answers. Submit this assignment using Google Docs or through email using scanned images or pictures. I. A student submitted the following work that shows the use of I'Hospital's rule: 10x x - 0ex + sin(x) By I'Hospital's rule: I'm = Then evaluating at x = 0; En 19 = 5 First use a graph to verify that lim 10x x + 0ex+sin(x) # 5 and is, in fact, equal to zero. Then clearly explain the error the student made that resulted in them achieving an incorrect answer. 2. In physics one learns that all objects fall at the same rate when there is no air resistance, When there is air resistance, velocity is slowed down according to the formula shown below. Suppose an object has a mass m and is dropped where the air resistance is A (both m and A are assumed to be constants and you do not need to be concerned with their units for this problem). Velocity at time tis: v(t) = (1 -e-At/m) where y is the constant acceleration of gravity. (a) Even if we let this object drop forever, it will have a finite maximum velocity (this is called the "terminal velocity"). Find the formula for an object's terminal velocity: lim " v (1) = t- 00' (b) In a vacuum there is no air resistance so A = 0. Suppose we fix a time f (so i is now assumed to be constant), find the formula for an object's velocity in a vacuum: lim A - 0+(t) =