Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.                                                                If f(x) = g(x) for x ≠ c and f(c) ≠ g(c), then either f or g is not continuous at c.

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

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Q: Q3. Let g : [a, b] → R is continuous function such that S° lg(x)| dx = 0.Determine g(x).(Justify…

A: g is zero constant function.

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Q: (c) If f(x) is continuous on a closed interval [a, b] and f(x)dx > 0, then f(x) > 0 for some x E [a,…

A: Since you have asked multiple questions in single request.so we will answering only first question.…

Q: (b) Test the continuity of the function f(x) = sgn(]x|) at x = 0. Is f(x) differentiable at x = 0?…

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A: Let (X, ΤX) and (Y, ΤY)be topological spaces A function f : (X, ΤX) → (Y, ΤY) is continuous  if…

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Q: Determine whether the statement is true or false. If f and g are continuous on [a, b], then f(x) dx…

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Q: Let the functionf be continuous on the closed interval [a, b] and differentiable with derivative f'…

A: From the definition of Rolle's theorem,

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A: To Determine whether the statement is true or false. Statement : All continuous functions have…

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Q: IV. Exercises Determine if the following functions are continuous at the given value of x. 1. f (x)…

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Q: (a) Use the definition to prove that f(x) = is uniformly continuous on the x +1 domain [0, 00). x- 2…

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Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A: Given        If f and g are continuous on [a,b] then∫abf(x) g(x) dx=∫abf(x)dx ∫abg(x)dx

Q: The sketch that represents a continuous function, y = f(x), such that: f'(-3)=Ø f(-3) = 5 and A(1) =…

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Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

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Q: True or false. Assume f is a continuous function on [a, b]. n (a) | f(x) dx = lim f(xi) · Ax a i=1…

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Q: A function f(x) is said to be continuous at x = c if the following three conditions are satisfied:…

A: Solution

Q: Using the graph attached a. Is f continuous at x = -2 ? Explain using the definition of…

A: We have to check continuity of given graph at x=-2 , x=1 and x=0.Graph is given below:

Q: Let f and g be continuous functions such that: [Fox f(x) = 3 And So, determine the value of: [2f(x)…

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Q: f(x) = {*- Įx² +px + 2,x # 3 3, x = 3

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A: Given , When function  F(x) is called an antiderivative of a function of f(x).

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Q: Which of the following functions does NOT satisfy the statement "If a function is continuous at x =…

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Q: example (with justification) of a function f : R→R which is continuous at exactly two points.

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Q: . Determine the value of c such that the function remains continuous. Draw your resulting function…

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Q: Let f be a continuous function and a < b. Show that: b -a f(-x)dx = | f(x)dx a -b

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Q: If possible, find numbers a and b so that fis continuous at every point x. x3

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Q: r(x) = -is continuous at every point in its domain.

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A: (I) For x=-1: LHL=limx→-1-f(x)        =limx→-1-1        =1 RHL=limx→-1+f(x)        =limx→-1+(-x)…

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A: Given f(x) = k

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A: Let f and g be the continuous functions such that fx≥gx for all a≤x≤b. It is known that the area…

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A: Given that f and g are two continuous functions on [a, b].

Q: Determine what, if any, value to assign to f (a) to make ƒ continuous at x = a. 3 f(x) = 2x2-x ;a =…

A: Note : as per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: x? + 2x + 1, if x 1. is continuous at x = 1 or not by using the definition of continuity.

A: f(x) = x2+2x+1  , if x≤14-x           , x &gt;1for a function to be continious at x = alimx→a+f(x) =…

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Q: Theorem: Let f,g€ C(X)are continuous function then 4) tf is continuous function and (tf)(x) = tf(x)…

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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.