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x 3+ (e) Let h = f+ 2g. Does lim h(x) exist? If so, find it. If not, explain why. x →3 (f) Is there a way to define f(3) such that h(x) has a continuous extension to x = 3? If so, find what value f(3) should have so that h(x) has a continuous extension to x = 3. If there is no such value, explain why. . The domain of f is R y = -1 is an asymptote of f. lim f(x) does not exist x4-2 ● f is right-continuous at x = -2 • f(1) = 2 ● -3 -2 -1 2. Sketch the graph of a function f(x) that has the following properties. Identify and label all asymptotes in your graph. (Use of pencil or another erasable writing method is highly recom- mended! You may need to backtrack quite a lot while doing this problem.): 4. Find the equations of all -1 -2 -3 • lim f(x) = 3 818 3. Find the equations of all asymptotes of the function f(x) = of limits, why a particular line is an asymptote. -4 -5 • f has an infinite discontinuity at x = 1 • f is increasing on the interval (1, 2) • fis decreasing on the interval (2,00) 1 2 3 |x + 1 2x - 3 Be sure to justify, in terms

x 3+ (e) Let h = f+ 2g. Does lim h(x) exist? If so, find it. If not, explain why. x →3 (f) Is there a way to define f(3) such that h(x) has a continuous extension to x = 3? If so, find what value f(3) should have so that h(x) has a continuous extension to x = 3. If there is no such value, explain why. . The domain of f is R y = -1 is an asymptote of f. lim f(x) does not exist x4-2 ● f is right-continuous at x = -2 • f(1) = 2 ● -3 -2 -1 2. Sketch the graph of a function f(x) that has the following properties. Identify and label all asymptotes in your graph. (Use of pencil or another erasable writing method is highly recom- mended! You may need to backtrack quite a lot while doing this problem.): 4. Find the equations of all -1 -2 -3 • lim f(x) = 3 818 3. Find the equations of all asymptotes of the function f(x) = of limits, why a particular line is an asymptote. -4 -5 • f has an infinite discontinuity at x = 1 • f is increasing on the interval (1, 2) • fis decreasing on the interval (2,00) 1 2 3 |x + 1 2x - 3 Be sure to justify, in terms

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you please help me sketch a graph for #2
x 3+ (e) Let h = f+2g. Does lim h(x) exist? If so, x →3 find it. If not, explain why. (f) Is there a way to define f(3) such that h(x) has a continuous extension to r = 3? If so, find what value f(3) should have so that h(x) has a continuous extension to x = 3. If there is no such value, explain why. -3-2-1 . The domain of f is R y = -1 is an asymptote of f. lim f(x) does not exist 412 ● f is right-continuous at x = -2 • f(1) = 2 2. Sketch the graph of a function f(x) that has the following properties. Identify and label all asymptotes in your graph. (Use of pencil or another erasable writing method is highly recom- mended! You may need to backtrack quite a lot while doing this problem.): -1 -2 -3 -4 -5 3. Find the equations of all asymptotes of the function f(x) = of limits, why a particular line is an asymptote. • f has an infinite discontinuity at x = 1 • f is increasing on the interval (1,2) • fis decreasing on the interval (2,00) • lim f(x) = 3 818 4. Find the equations of all asymptotes of the function f(r) terms of limits, why a ponti 1 2 3 |x| +1 2x - 3 Be sure to justify, in terms VI +
Transcribed Image Text:x 3+ (e) Let h = f+2g. Does lim h(x) exist? If so, x →3 find it. If not, explain why. (f) Is there a way to define f(3) such that h(x) has a continuous extension to r = 3? If so, find what value f(3) should have so that h(x) has a continuous extension to x = 3. If there is no such value, explain why. -3-2-1 . The domain of f is R y = -1 is an asymptote of f. lim f(x) does not exist 412 ● f is right-continuous at x = -2 • f(1) = 2 2. Sketch the graph of a function f(x) that has the following properties. Identify and label all asymptotes in your graph. (Use of pencil or another erasable writing method is highly recom- mended! You may need to backtrack quite a lot while doing this problem.): -1 -2 -3 -4 -5 3. Find the equations of all asymptotes of the function f(x) = of limits, why a particular line is an asymptote. • f has an infinite discontinuity at x = 1 • f is increasing on the interval (1,2) • fis decreasing on the interval (2,00) • lim f(x) = 3 818 4. Find the equations of all asymptotes of the function f(r) terms of limits, why a ponti 1 2 3 |x| +1 2x - 3 Be sure to justify, in terms VI +
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