Define h as x < 2 (3x – 2 x > 2 Determine whether the function h is continuous h(x) = {3, x2 or discontinuous at x = 2.

Q: Assume that a continuous function f:R → R is X- and µ-periodic, where A and u are two nonzero…

A: We know that between two rational number lies infinite many irrational number. But function is…

Q: Let f : R² → R defined by f((x1, x2)) = x1 - x2. Then determine if is Lipschitz continuous(if it is,…

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Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0, -2 < h(x) < 2 for all x,…

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Q: Find the constant a such that the function is continuous on the entire real line. [ 5x², x 2 1 x < 1…

A: The given function is: f(x)=5x2   ,   x≥1ax-3,  x&lt;1 To find constant 'a' such that the function…

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: Consider the piecewise function 2+x² x<0 x=0 g(x) = 1, 2-³, 0<x< 1 2-x x 21 (a) For each of the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Let the function f(x) be defined by: 2x – 6 x + 3 f(x) = {Vx – 1– V2 2 x = 3 Determine the…

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Q: Find the constant a such that the function is continuous on the entire real line. x 21 f(x) = lax –…

A: The function is continuous on the entire real line. We have to find the value of a.

Q: 9-x - S(x)= Vx- 6

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Q: Determine the values of a and b such that the function (x -a ,x 1 Is continuous of all values of x.

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Q: D. Prove that f(x) = |x - 6| is continuous at all points c in R.

A: Given function is fx=x−6. We have to prove that the function fx=x−6 is continuous at all point c in…

Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

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Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: Determine if the given function is continuous on the given interval a. [2,5) , x <O f(x) = %3D 5x-8…

A: To determine whether the given function is continuous on the given interval.Interval=[2, 5)fx=1x,…

Q: Suppose that f (x) = x·g(x) for some function g that is continuous at 0. Prove that f is…

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Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = cosx2 /…

A: f(x)=cosx2x2-1

Q: f is continuous at a if and only if |f| is continuous at a.

A: False

Q: Discuss the continuity of the function g(x). 1 +- x 2 Vx- 2, Identify if the function g(x) is…

A: To check the continuity at x=1 we will find limx→1-g(x) and limx→1+g(x).…

Q: Find all values of "c" such that the function f(x) is continuous over  ( − ∞ , ∞ ) f(x) = 1 - x^2…

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Q: Suppose f : R → R is a continuous function with the property that f(x) = 0 for every x E Q. Prove…

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Q: Sketch the graph of a continuous function y = h(x) such that a. h(0) = 0,–2 < h(x) < 2 for all x,…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: Assume that g : R → R is a periodic continuous function. Prove that f(x) = 2x + g(x) is uniformly…

A: The complete solutions are given below

Q: Let f be a continuous function on R such that f(x+y)=f(x)+(y) ¥x, yER. Show that f(x)3cx for some…

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Q: Assume that ƒ is continuous on [0,1] and that f(0) = 2 and f(1) = 1. Show that the graph of y = f(x)…

A: given  f is continuous on [0,1] f0=2,f1=1y=x2+1

Q: Sketch the graph of a continuous function y = f(x) such that : a. g(2) = 2,0 2, and g'(x) →-1* as…

A: (a)  Find the behavior for g (x).

Q: Let a be a real valued constant. Find f' (x) = limħ→0 f(x+h)-f(æ) for f (x) = Vax h

A: Given, α be a real valued constant.  fx =αx  We have to find f'x = limh→0fx+h-fxh

Q: 8. Suppose that f is a continuous function with f(x) > 0 for all real numbers x, and lim f(x) = 0 =…

A: Consider the provided question, Suppose that f is a continuous function with f (x)&gt;0 for all real…

Q: 2. Determine whether f is continuous or discontinuous at 1. (x – 1 if x > 1 f(x) -x² if x <1 O f is…

A: Given query is to find function is continuous or not at x = 1.

Q: Determine if g (r)= is continuous at a = 8.

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Q: Prove that the following continuous function has at least one real root; h(x) = −2x + 3 − ln x

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

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Q: 1. Determine whether k(x) is continuous at a = 3, where x + 3, x 2.

A: Left-hand limit of f(x) at x=a is represented by limx→a- f(x) and it can also written as limh→0+…

Q: Find all values of a such that f is continuous on R: |x + 1 if x a

A: For a continuous function LHL ( left hand limt) should be equal to RHL (right hand limit)

Q: Determine whether the function f(x) = (2x + 1)/(2x2 - x - 1) is continuous: a) at 2; b) at 1.

A: It is given that, fx=2x+12x2-x-1We have to find that the function is continuous at   a 2 and b 1

Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: 4. Let f:R→ R be a function defined by f(x)=x for every xeX . Show that f is a continuous.

A: Let A ⊆ R , let f:A → R and let c ∈ A. We say that f is continuous at c if, given any number ε&gt;0,…

Q: Find c such that the function ² - 4 x c is continuous everywhere.

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Q: Determine if g (x) = is continuous at x = 0

A: A function f(x) is continuous at x=a if, limx→af(x)=f(a). We try to evaluate limx→04-xx and f(0) and…

Q: x + 6|, if x - 1 x² – 3x

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Q: Consider the continuous function h with h'(x). In(x) +6 3 3.1 Find and represent the domain of the…

A: We have to find domain

Q: 45. Let f : R → R be a continuous function, such that f(x)= 0 if x is a rational number. Show that…

A: Given continuous function is f: ℝ → ℝ such that f(x) = 0 if x is a rational number.

Q: Find the values of a and b such that the following function f(x) = 2a cos(x + 1) - b.5x+2, if x -1,

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Q: x 2

A: Consider the function f(x)=x-1              ,       x≤02x2-3x+1    ,       0&lt;x≤23x3-x2          ,…

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: Prove that there is no continuous function f : S² → S' such that f(-x) =-f(x) for all x € S².

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