8. A function fis continuous at the point X=a if the following conditions are satisfied. 1.f(a) is defined. 2. limf(x) exists. 3. limf(x)-f(a), Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated. (2x -3 ifx s2 f(x) = (4 if x >2 O -2 -1, 10:25 PM 61°F 9/23/2021 ype here to search acer 立

Q: II. Prove that for each of the following lim (x,y)→(0,0) f(x, y) does not exist. ,2,,2 4. f(x,y) x4…

A: limx, y→0, 0x2y2x4+y4

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Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

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Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

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Q: 8) Suppose if x 20 f(r) = if x < 0. Identify a function g with domain R such that lim(f +g)(x)…

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Q: B) Evaluate two of the following limits (Without using calcu 1 1) lim 1-cos2 x

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Q: Let f(x)={−2x+2   x≠1               {−5         x=1. What is f(1)? If f(1) does not exist, type:…

A: Given,

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A: To determine: The limit

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A: Given query is to find the wrong statement.

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Q: Prove that a function f is continuous at a limit point p iff the limit as x goes to p is f(p).

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Q: . Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable…

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Q: -1– x + 5 if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: limx→-2-f(x)=6, limx→-2+f(x)=6,  and limx→-2f(x)=6

Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

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Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

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Q: (4- x - x² if x ≤ 2 2x-7 if x > 2 Calculate the following limits. Enter "DNE" if the limit does not…

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Q: 8- x- x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x)…

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Q: (4) Find the values of a and b so that h(x) is continuous at = 4. Hint: Write down the limit…

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Q: if x — 4 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x→ –…

A: a)

Q: 2 – x x2 if x 5 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

A:

Q: 10. Prove that the statement "If lim f(r) exists, then f is continuous at a" is false by using a…

A: See the solution below.

Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x.y)-(0,0) x²+y2

A:

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=…

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Q: Suppose the functions ƒ(x) and g(x) are defined for all x and thatlimx→0 ƒ(x) = 1/2 and limx→0 g(x)…

A: Given limx→0fx=12 and limx→0gx=2we have to findfx.cosxx-1

Q: 37. The function / has a removable discontinuity at z„. Therefore A S(7,) exists B lim f(z) exists C…

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Q: 11. Show that the limit lim (z.y)→(0,0) r² + y4 does not exists.

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Q: 1) Show that the limit doesn't exists : 3x2 Jy 2). lim (x,y)→(0,0) x2 +y²

A: We have considered different paths y = mx. If the limit is independent of m then the limit shall…

Q: [ 2 Let f(x) x – x2 if x 3 - Calculate the following limits. Enter "DNE" if the limit does not…

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Q: 58. If f(xo, Yo) 3, what can you say about lim f(x, y) (x, y)→(xo, Yo) if f is continuous at (xo,…

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Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

Q: 8) Suppose if r 20 if r < 0. f(r) = Identify a function g with domain R such that lim(f+g)(x) exists…

A: The explanation is as below

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Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x =…

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

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A: see below the answer

Q: 4. a) Explain using theorems from Section 2.5 why the function is continuous at every number in its…

A: We have to solve given questions.

Q: (b) Use the sandwich theorem to show that limy0x°cos - = 0. 1 In order to apply the sandwich…

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Q: x+4 Which will prove that f(x) is continuous at C= -4? x2+16 1. f(-4)=0 II. lim f(x)=0 III. f(x)=…

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Q: if r =-1 A if z + -1 2. Is f(r) = continuous at r =-1? (Show your work using limits.)

A: