Find all values of a such that f is continuous on R: |x + 1 if x< a |x² f(x) if x> a

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: 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: 5. Let f : R → R be defined by f(x) = { 0 if r € Q, x2 otherwise. Prove that f is continuous at 0…

A: Here we prove the problem using the definition of continuity and a theorem.

Q: Provide a function f, continuous on (0, 1), such that for all r where f'(x) exists, f'(x) > 0 but f…

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Q: If f is continuous at a, then f is differentiable at a. O True O False

A: Answer: False.

Q: Let f and g be continuous functions on the interval [a,b], such that f(x)=g(x)-1 for all asx<b.…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Where is f(x) = x-5 x² –6x+5 discontinuous? f (x)is continuous everywhere o 5 o 1 о 5, 1

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

A: The given function is  kx=x+3 , x&lt;0x2+1, 0≤x≤22x,      x&gt;2 A function f(x) is said to be…

Q: Prove that the function f(x) = 2x is uniformly continuous on R.

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Q: Find a value of a so that f is continuous at c = -3, or indicate this is impossible. x+3 x -3 f(x) =…

A: Given the function   f(x) = x+3-5x+3,  x≠-3a,                 x =-3   We need to find the value a…

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: Find a value of x, if any, at which f(x) = x + 2 - is not continuous. x2 + 4 If f(x) is continuous…

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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: Let f be continuous on [a, b] and suppose that f(x) 2 0 for all x e [a,b]. Prove that if L(f)=0,…

A: Given: Let f be continuous on [a,b] and suppose that f(x) is greater than or equal to zero for all x…

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

A: False

Q: Let f(x) be a piecewise function defined as follows, where a, b, and c are constants: ае* + x + 1 if…

A: the solution is given below

Q: Find all values of c such that f is continuous on (-0, 0). 1- x2, f(z) = { – x², x. C = (smaller…

A: Given function is, fx=1-x2   , x≤cx          ,x&gt;c  Since 1-x2 and x are continuous on the…

Q: Find all values of c such that f is continuous on (-00, 00). f(r) = { 8 – x², !! x>c

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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: Find the constant a such that the function is continuous on the entire real lin Sex², f(x) = x 2 1…

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Q: 2: If f(x) and g(x) are continuous on (a,b]and if f =[s . Prove that 3cela,b] such that f(c)=g(c).…

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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: Find the values of a and b that make f(x) continuous for all real x.(Note:the functions are…

A: Given, f(x)=bex+a+1,               x≤0ax2+b(x+3),         0&lt;x≤1acos(πx)+7bx,            x&gt;1…

Q: If a function f(x) is not defined at x-a, then it is not continuous at an open interval (a, b) * O…

A: Given Statement is "False"

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

A:

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: . Find a value of k so that the following function is continuous at x = 1. f(x)%3D x<1 x-1 2kx, x21

A: Given: The given function                                             To find: The value of k, such…

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: 4. Suppose that f is continuous on a closed interval [a, b] and differentiable on the open interval…

A:

Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: 1 - is continuous at a. f If f(x) 0 for all x in the interval I, and f is continuous at a in I then…

A: 1/f is rational function this is discontinous where either f is discontinous or f is zero  But f is…

Q: Let ƒ : R → R be a continuous function such that f(0) 0. Prove that f(1)< 1 for all real x.

A: given f:ℝ→ℝ is a continuous function such that f(0)≤1 for all real x f(x)2-3f(x)+2≥0 to prove f(1)≤1…

Q: Find all values of the constant a such that f is continuous for all real numbers. ах x 2 0 f(x): tan…

A:

Q: If f is a continuous function on [a, b], and if f (a) = -2 and ƒ (b) = 2, then there exists a real…

A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

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 values of x, if any, at which f is not continuous. Prove using limits. f(x)= x/x^2 +4

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Q: Let f(x) be a given continuous function on a closed interval [a, b]. Use the Extreme Value Theorem…

A: given fx is a continuous function on a closed interval a,b to prove- use extreme value theorem to…

Q: 15. Let f, g : R → R be continuous at a point c, and let h(x) = sup (f (x). 8(x)} for x e R. Show…

A: A function is one-one means if the value of the domain are equal then the value of the range set…

Q: Let f be a continuous function defined on E. Is it true that f^-1(A) is always measurable if A is…

A: Prove the given statement

Q: x + 6|, if x - 1 x² – 3x

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Q: If f(x) is a continuous function such that it is increasing on [1, 3], then Si f(x)dæ is less than…

A:

Q: 4. Let A := (0, 1] and let f : A → R be defined by f(x) = !. Prove that f is continuous on A.

A:

Q: Let A := (0,1] and let f : A → R be defined by f(x) = . Prove that f is continuous on A.

A: Consider the provided question,

Q: If f(x) is continuous on a closed interval I, and f(a) and f (b) have opposite signs where a and b…

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Q: Show that the function f:R to R defined by f(x)=5x-12 is continuous using the E-d definition

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Q: Every continuous function on R satisfies the conditions of MVT. * False True

A: We have to evaluate that the statement, ''Every continuous function on R satisfy the conditions of…

Q: Let f(x) be a given continuous function on a closed interval [a, b]. Use the Extreme Value Theorem…

A: Extreme value theorem: A continuous function on a closed and bounded interval is bounded. Bounded…

Q: If f is a continuous function on R with (1) > 0 and f(4) < 0, then there exists a number c between 1…

A: In this question, we need to check whether the given function is true or false.

Q: Show that f(x) = 1/x2 is uniformly continuous on the set [1,∞) but not on the set (0, 1].

A: To show that f(x)=1x2 is uniformly continuous on the set [1,∞) but not on (0,1].

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.