Test the continuity of the function f(x): 3 — х X +1 2

Q: f(x) = V3x–1 c = 1

A: As we know that; If the function fx is continuous at x=c then, limx→c-fx=limx→c+fx=finite…

Q: Find the value of the constant k so that f(x) is continuous for all real values of x where f(x) is…

A: Solution

Q: Find the constant a such that the function sin x -13 - S(x) = %3D a+ 11x, x 20 is continuous on the…

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Q: Find c such that the function f(エ) 8x- 20 I > C is continuous everywhere.

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: Discuss the continuity of the function h(x) = }" (x2 + 7х -5, x3 – 2x2 + 1, x < 3 x 2 3 on the…

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Q: Test the continuity of the following functions at the indicated points of each x+ 1, 3x - 1, 1 < x <…

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Q: 1. For what value of k is the function h(x) continuous on the whole real line? HINT: Use definition…

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Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: Find the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x…

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Q: Find the constant a such that the function is continuous on the entire real line. S 8x², f(x) ax -…

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Q: Find the constant a such that the function is continuous on the entire real line. 4sin x if x < 0…

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Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: x+1 x 0 6-х the indicated test point. If it is discontinuous, specify the type of discontinuity.

A: We have to solve

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x <0…

A: For a function to be continuous at x = a, it must satisfy the following condition:

Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

A: Here, the given function is: f(x)=x2-4, if x≤c10x-29, if x&gt;c To find the value of c such that the…

Q: b. Test the continuity of the following function 1, V1-x,0sIs1, at x = 0,1 (x-2, x<0 x21

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Q: Find the constant a such that the function is continuous on the entire real line. (5x2, ах — 3, x 2…

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Q: 2. Test continuity at x = 0 and x = 3 for the function (3 + 2x; - 3 3

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Q: 3. f(x) = v2x – 5 at x = 3 -

A: (3) Given function is fx=2x−5 We have check whether the function fx is continuous or not at x=3 For…

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x if x < 0…

A: For continuity of f(x) LHL=RHL     so find lhl and rhl and equate both to get a.

Q: Find the constant a such that the function is continuous on the entire real line. 1 = √7x², lax - 5,…

A: Topic = Function

Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: Find the continuity of the function Of(x)= tx²+3 と+ とく3 5x-3 at =t

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Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: Discuss the continuity of f(x) = {Vx, x > 1 1, x<1 at x = 1.

A: A function f is said to be continuous at some point a if the value of the function at that point is…

Q: Determine the continuity of the function at the given points. f(x) = [1, x-2, for x=1 at x = 1 and x…

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Q: Discuss the continuity of the function f(r) at a = 0.

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Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+2, f(x) = { ax³, (x² +…

A: Given that f is a continuous function, then it is continuous at all the point. So, the function is…

Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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Q: Find the constant a such that the function is continuous on the entire real line. Ssin x g(x) = if x…

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Q: Test the continuity of the following functions at the indicated points of each (x+1, (1) f(x) = {3x…

A: f is continuous at x = 1  f is not continuous at x = 2 &amp;, f is continuous at x = 3/2   The…

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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Q: (c) Simplify the function f(x) = |x - 1|+ |x + 1|. Test the continuity of this function at x 1. At…

A: f(x)=|x-1|+|x+1|, for all x∈ R, It can be written as f(x)=-(x+1)-(x-1),       x&lt;-1(x+1)-(x-1),…

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: Q2/B/ check the function continuity at x-0, for the fimction f(x)%= 1+ 4 2/3

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Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

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Q: Q2) Discuss the continuity at x=2. When: x> 2 X = 2 x< 2 Зх + 1 f(x) = } x? + 3 %3D 2х + 1

A: Our objective is to discuss the continuity at x=2.

Q: Find the values of a and b that make f(x) continuous for all real numbers. (x+ 2, f(x) = { ax³, (x²…

A: f(x)=x+2,x≤-1ax3,-1&lt;x≤1x2+bx,x&gt;1

Q: Discuss the continuity of the function. x2 – 4 f(x) X + 2 f is discontinuous at x =

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Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

Q: x²-1 - 1 ion f(x)= %3D x-1

A: Definition use -             A function f(x) is continous  at x= a if…

Q: , for x 1 Let f(x) be a function defined by f(x)=- Discuss the contuniuty of f and f'.

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Q: 6. Discuss the continuity for the following functions x+y a) f(x,y) = 4x2-y2-4 x+y b) f(x, y) = %3D…

A: The objective is to discuss the continuity of the functions.

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: