The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = -4.Select all that apply:☐ f(x) is not continuous at x = -4 because it is not defined at x = −4.☐f(x) is not continuous at x = -4 because lim f(x) does not exist.x-4f(x) is not continuous at x = -4 because lim f(x) = f(−4).☐ f(x) is continuous at x = -4.x-4ين من طلب نہ1 2 3 4 5 6 7

To determine the continuity of f(x) at x = -4 , let's analyze the graph: 1. Is f(-4) defined?-…

Answered: The graph of f(x) is given below.…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 48E

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The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 3. Select all that apply: 7 -6- 5 4 3 2 1- -7-6-5-4-3-2-1 1 2 3 4 5 6 7 +1 -2· 3. -4 -6- f(x) is not continuous at a = 3 because it is not defined at x = 3. ☐ f(x) is not continuous at a = - 3 because lim f(x) does not exist. 2-3 f(x) is not continuous at x = 3 because lim f(x) ‡ ƒ(3). →3 O f(x) is continuous at a = 3.
Let a and b represent real numbers. Define ax² + x - b, ax + b, 2ax f(x): a = b = (a) Find the values of a and b such that f is continuous on the entire real number line. (c) Let g(x) - (b) Evaluate lim f(x). X→ 3 Need Help? Submit Answer 7, = f(x) x - 1 if x ≤ 2 if 2 < x < 5. if x 25 Read It Evaluate lim g(x). X→1
Use the definition of continuity, along with the One- sided continuity theorem, to determine whether the following function is continous at x=4. Also discuss whether the function is left-continuous and/ or right-continous at 4. f(x)={3 if x=4 {|3x-12|/x-4 if x not equal to 4 Refering to graph or a table of value will earn zero credit.
. The function f (x) is defined by the rule 2-36 if x + 6 f (x) x-6 25 if x = 6 (a) Calculate lim f (x). x-6 (b) Use the definition of continuity to show that f is discontinuous at c = 6.
If f is C2 on an interval prove that lim h-0 f(x + h) – 2f(x) + f(x - h) h2 = f" (x). The expression f(x+h) – 2f (x)+ f(x-h) is called the symmetric second difference.
Let g(x) be the following piecewise-defined function: 9 – x2 if x -3 g(a) = 2(x + 3) B2 if x = -3 Determine the values of B that make the function g(x) continuous at x = -3. You must justify your work using limit/continuity definitions. (next page) Aa
The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = -1. 654 -2- -7-6-5-4- 2-1 1 2 5 6 7 02. Select all that apply: ☐ f(x) is not continuous at x = -1 because f(-1) is not defined. ☐ f(x) is not continuous at x = −1 because lim f(x) does not exist. x-1 ☐ f(x) is not continuous at x = −1 because lim ƒ(x) ‡ ƒ(−1). ☐ f(x) is continuous at x = -1 J-←台

The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = -1. -7-6-5 N HT Select all that apply: ☐ f(x) is not continuous at x = -1 because it is not defined at x = -1. ☐ f(x) is not continuous at -1 because lim f(x) does not exist. x-1 ☐ f(x) is not continuous at x = -1 because lim f(x) = f(−1). ☐ f(x) is continuous at x = -1. x-1 5 6 7
Use the graph of the function f shown below to respond to each prompt. The first prompt is worth 3 points. The other prompts are worth 0.5 points each: 10-9-8--6-5-4-3-2 ● Does Not Exist Undefined x→-3 lim x-3 . Can be found, lim f(x) lim x → 1 Does Not Exist Undefined f(x) = lim f(x) x →1 . Can be found, f(x) = The function has several discontinuities. State the location of two discontinuities and explain, using the definition of continuity, why the function is not continuous at that location. Does Not Exist Undefined f(- 6) 10+ 9 Edit Insert Formats B IU X₂ X² A E = = E- 3? e & N lim f(x) x+3+ . Can be found, lim f(x) = x+3+ 8+ f(-3) f(-7) . Can be found, f(-7)= . Can be found, f(-3) = Does Not Exist Undefined 7 6 5 4- 3 2 1 -2 -3 -4 -5 -6 -7 -8 9+ --10+ 2 A I V 4 5 6 7 8 9 10 Does Not Exist Undefined lim x →-3+ 。 Can be found, lim f(x) x → f(x) = - 3+ Does Not Exist Undefined f(1) Can be found, f(1) = Does Not Exist Undefined lim f(x) x →3 . Can be found, f(x) = lim x →3 Does Not…

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