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Q.#9 For above function, please find and classify any other removable or non-removable discontinuities elsewhere in the function. If non-removable, classify them as jump or infinite. Hint: Normally one checks transition point(s) and the functions themselves. Q. #8 checked the transition point (x= -1), so leaves only the functions themselves. Final Answers Function 3 1-x for x < -1 a) f(x)=- b) f(x) = 1 for x=-1 x-2 ²-4 for x>-1 Continuous where applies? (Y/N) Discontinuous where applies: At x= Removable Non-removable: Jump Non-removable: Inf.

Q.#9 For above function, please find and classify any other removable or non-removable discontinuities elsewhere in the function. If non-removable, classify them as jump or infinite. Hint: Normally one checks transition point(s) and the functions themselves. Q. #8 checked the transition point (x= -1), so leaves only the functions themselves. Final Answers Function 3 1-x for x < -1 a) f(x)=- b) f(x) = 1 for x=-1 x-2 ²-4 for x>-1 Continuous where applies? (Y/N) Discontinuous where applies: At x= Removable Non-removable: Jump Non-removable: Inf.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I have question 8 done however you need the function from question 8 to do question 9 and 10. Please help I am new to calculus and I’m struggling
Q. #8-Q.#10 Please use the function shown at the right for these questions. Q.#8 For this function, please do the following. a) Use the definition of continuity to determine algebraically if f(x) is continuous at x = -1. lim f(x) = lim f (1-1) = lim X→-|- ho Tim X-X(-1) lim x=-1+ f(x)=lim f/-1+h) - lim -1th-2 ~ 1+h-2² - ²³/3 = 1 h-₂0 (++)³-4 -3 hoo # fix) "F(X) is not continuous ut x==1₁₁0 b) If a discontinuity at x = -1, classify it as removable or non-removable. If non-removable, is it jump or infinite ? f(x) lim fcx) X-→-- hao 1-(1-6) but not f (x) lim +1+ and lim f(x) junx-(-it =lim 3 h-2 3 th=3 f(x)= both exists continuity 3 1-x , for x < -1 1, for x = -1 x-2 x²-4 for x>-1 Final Answer (yes or no) по Final Answer (circle) No discontinuity equal. So, f(x) hus non-removable discontinuity there fore hus jump discontinuity. Removable Non-removable: Jump, Inf. Page 2 of 8
Transcribed Image Text:Q. #8-Q.#10 Please use the function shown at the right for these questions. Q.#8 For this function, please do the following. a) Use the definition of continuity to determine algebraically if f(x) is continuous at x = -1. lim f(x) = lim f (1-1) = lim X→-|- ho Tim X-X(-1) lim x=-1+ f(x)=lim f/-1+h) - lim -1th-2 ~ 1+h-2² - ²³/3 = 1 h-₂0 (++)³-4 -3 hoo # fix) "F(X) is not continuous ut x==1₁₁0 b) If a discontinuity at x = -1, classify it as removable or non-removable. If non-removable, is it jump or infinite ? f(x) lim fcx) X-→-- hao 1-(1-6) but not f (x) lim +1+ and lim f(x) junx-(-it =lim 3 h-2 3 th=3 f(x)= both exists continuity 3 1-x , for x < -1 1, for x = -1 x-2 x²-4 for x>-1 Final Answer (yes or no) по Final Answer (circle) No discontinuity equal. So, f(x) hus non-removable discontinuity there fore hus jump discontinuity. Removable Non-removable: Jump, Inf. Page 2 of 8
Q.#9 For above function, please find and classify any other removable or non-removable discontinuities elsewhere in the function. If non-removable, classify them as jump or infinite. Hint: Normally one checks transition point(s) and the functions themselves. Q.#8 checked the transition point (x= -1), so leaves only the functions themselves. Final Answers Function 3 1-x for x < -1 a) f(x)=- b) f(x) = 1 c) for x = -1 x-2 ²-4 for x>-1 Continuous where applies ? (Y/N) Discontinuous where applies: At x= Non-removable: Jump Removable Non-removable: Inf. Q.#10 Using any discontinuities in Q.#8 - Q.#9, please list the intervals of continuity for f(x). Example: If a function has removable discontinuity at x=2, its intervals of continuity are (-0, 2) (2, +∞0) or, equivalently, (xx<2ux>2) or (x|x=2} Final Answer Page 3 of 8
Transcribed Image Text:Q.#9 For above function, please find and classify any other removable or non-removable discontinuities elsewhere in the function. If non-removable, classify them as jump or infinite. Hint: Normally one checks transition point(s) and the functions themselves. Q.#8 checked the transition point (x= -1), so leaves only the functions themselves. Final Answers Function 3 1-x for x < -1 a) f(x)=- b) f(x) = 1 c) for x = -1 x-2 ²-4 for x>-1 Continuous where applies ? (Y/N) Discontinuous where applies: At x= Non-removable: Jump Removable Non-removable: Inf. Q.#10 Using any discontinuities in Q.#8 - Q.#9, please list the intervals of continuity for f(x). Example: If a function has removable discontinuity at x=2, its intervals of continuity are (-0, 2) (2, +∞0) or, equivalently, (xx<2ux>2) or (x|x=2} Final Answer Page 3 of 8
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