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Math 171 — Calculus I Spring 2016 Name: 1 Weekly Write-Up on Sections 2.1-2.3 Problem 1. From the suggested homework: [2.2 #53] Sketch the graph of the function with the given limits. lim f (x) = f (2) = 3, lim− f (x) = −1, lim f (x) = 2 6= f (4). x→2+ Problem 2. x→4 x→2 From an old exam: The fungus Fusarium exosporium infects a field of flax plants through the roots and causes the plants to wilt. Eventually, the entire field is infected. The percentage f (t) of infected plants as a function of time t (in days) since planting is shown in the figure below. a. What are the units of the rate of change of f (t) with respect to t? b. Which interval [0, 10], [20, 30], or [40, 50] has the largest average infection rate? Circle one: [0, 10] [20, 30] [40, 50] c. Which interval [0, 10], [20, 30], or [40, 50] has the smallest average infection rate? Circle one: [0, 10] [20, 30] [40, 50] 2 Problem 3. For in-class discussion: Light waves of frequency λ passing through a slit of width a produce a Fraunhofer diffraction pattern of light and dark fringes (see figure). The intensity as a function of the angle θ is 2 sin(R sin θ) I(θ) = Im R sin θ where R = πa/λ and Im is a constant. Show that the intensity function is not defined at θ = 0. Then choose any two positive values for R check numerically that I(θ) approached Im as θ → 0. ±1 ±.1 ±.01 ±.001 ±.0001 R= θ I(θ) θ I(θ) ±1 ±.1 ±.01 ±.001 ±.0001 R=