What values must a and b take for f to be continuous everywhere?

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

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Q: For what value of a is the following function continuous at every x? f(x): a²x-2a, x≥2 X<2 12,

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Q: Is the following statement correct? If the function is continuous on R then the constants a and b…

A: It is not necessarily correct that every continuous function on R take the value 2&amp; -2…

Q: 2.

A: A function is said to be continuous if its graph is not split or break at any point of the domain.…

Q: Find the values of c that makes the function continuous on R -cz² + c² ifz < 5 f(x) = 8c – 822 if æ…

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Q: A function is said to be continuous where t = 7, can this same function be discontinuous anywhere…

A: Consider a function        f(t) = t + 8 ,     if t ≤ 7                  22 - t,     if 7 &lt; t ≤ 8…

Q: (a) A function is continuous from the left at a if (b) A function is continuous from the right at a…

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Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: Find the values of a and b that make the following function continuous. f(x) { 8x if x 2 7x What is…

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Q: xux-yuy+y2u=y2x find the general solution

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Q: 3. Let f : A → B. Then 18f = f and f1a = f. Hint. You may use the fact that fg, for functions f, g,…

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Q: Suppose f is a continuous function with x = a in its domain. Part 2 of the Fundamental Theorem of…

A: Note:- As per our guidelines, We’ll answer the first question since the exact one wasn’t specified.…

Q: Provide an example of function f: R → R which is continuous at exactly one point and discontinuous…

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Q: 4x-8 i- -2 x +3a

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Q: How many one-to-one functions f: [4] to [6] have 5 not in the range of f?

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Q: Determine the values of m and b such that function g is continuous at every real number: if r 1.

A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

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.