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Week 8 Solution

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Mathematics
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Grantham University
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Homework
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Surname 1 Student's Name Course Instructor Course Name Date Due 1) Using the chart, approximate the limit of the function f(x) = sin x/ x as x Approaches zero. Note the numbers are in radians: x -1 -0.25 -0.01 -0.005 0.005 0.01 0.25 1 f(x) 0.8415 0.9896 0.9999 0.9999 0.9999 0.9999 0.9896 0.8415 2) Using a method like 1 above, approximate the limit of the function f(x) = (1 + x)(1/x) as x approaches zero to three decimal places. What famous number does this limit approach? Solution 1 = lim(1 + 𝑥)( ) 𝑥→0 𝑥 lim(1/𝑥 + 1) = ∞ 𝑥→0 Hence the limit does not exist 3) Using the graph of a function f(x), determine the limit of the function as x approaches 1. Surname 2 Answer lim = 2 𝑥→1 As in the graph at x= 1 then y=2 satisfies in the graph 4) The following is the graph of a function which is not defined for x = 2. Using the graph determine the limit of the function as x approaches 2. Solution lim = +1 𝑥→2+ And lim = −1 𝑥→2− Surname 3 So the limit are not equal and does not exist 5) Determine the limit of the function as x approaches infinity: 𝑓(𝑥) = 2𝑥 2 𝑥2 − 9 Solution lim ( 𝑥→∞ 2𝑥 2 ) 𝑥2 − 9 = 2 ∗ lim ( 𝑥→∞ 𝑥2 ) 𝑥2 − 9 Dividing by the highest denominator power = 1 9 1− 2 𝑥 lim 1 =2* lim𝑥→∞ 1−9/𝑥^2 𝑥→∞ =2 Solution lim (9𝑥 2 + 45𝑥) 𝑥→−5 Surname 4 Substituting the value x=-5 =9(-5) ^2 +45(-5) =0 Hence (e) is the co ...
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