Name: MCV4U Rates of Change Assignment Expectation: demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit. 1. Given a function f and fa) is the value of the function when x - a. lim M.x) - na) x - a This quotient is an alternative to one of the most important quotients in Calculus. Explain what this quotient represents in terms of what you know so far about limits, average and/ or instantaneous rate of change. You may want to include a diagram/graph to support your explanations. 2. A function fis defined by the graph below. X -3 lim f (x) a. What is x-0 ? Justify your answer. lim f (x) b. What is x-2 ? Justify your answer. 3. A sequence has the terms: (1 + 7): (1 + 2)3(1 + 3). (1 +7).. Does the sequence have a limiting value? Justify your response (e.g., numerically, graphically using Desmos).Q W E R O VA A S U D O G P H C K B N M pause x2 + 4x +3 lim 4. Explain why evaluating x--1 x+1 requires algebraic x2 + 4x + 3 lim manipulation while evaluating x-+4 x +1 does not. 5. Create a unique function in rational form that has at least one discontinuity. Provide both the algebraic and graphical representations of this function. You can use Desmos to create the graphical representation. This function can have a radical in the numerator or denominator. Ensure that the limit exists at one of the discontinuities. Be creative. a. Show how to calculate the average rate of change between two points in the domain for this function. b. Show how to estimate the instantaneous rate of change at one point in the domain (e.g., using a centered interval, preceding interval, following interval, difference quotient). c. Apply appropriate techniques to evaluate the limit algebraically and graphically for: > One point in the domain for this function. > The removable discontinuity