Determine whether the statement is true or false. If f(x) is continuous at x = c, then so is f(x). True O False

Q: 2x Let f (x) = x+3 Then f is increasing over R*. False True

A: We will check for the sign of first derivative If f'(x)≥0 , then f(x) is increasing If f'(x)≤0 ,…

Q: c. Let f(x) = x > 2 is the f(x) is continuous at x=2. X-2 8, x< 2

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

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

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A: We need to find a.

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Q: find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Given: find the x-values (if any) at which f is not continuous. Which of the discontinuities are…

Q: x+2a, if x<1 What value for a would makef (x)continuous everywhere? Let f(x)= (ax? +7x-4, if x21

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Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

Q: Let f(x) be a function and be R. f is continuous at r = b if and only if : 4.1 ......... 4.2 4.3

A: Refer to the definition of continuity.

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A: Two continuous function fx and gx Let fx=aconstant, constant function is always continuous. gx=ax,…

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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: c. Let f(x) = } x-2 x > 2 is the f(x) is continuous at x32. %3! 8, x < 2

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Q: Let the function if I< 2: x +1 if Find values of a, b for that function to be continuous at x=-2 and…

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Q: Suppose f : [a, b] → R is is continuous and such that fg = 0 for all continuous functions g : [a, b]…

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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: Зх -5 S(x) = 2x? — х —3 х-3

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

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A: Given query is to find that function is continuous or not at given point.

Q: B- If f(x) = is continuous at x = Find A? |Ax2 x2

A: The explanation of the answer as follows

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A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Which value must you assign to a so that f(x) is continuous at x = 7? 7+ 6x - x? x+7 f(x) . x-7 a…

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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: Let f be a continuous function such that | = -2 and f (x) de -7 -2 f(2). dx = 3. What is the value…

A: Given that ∫-7-2 fx dx =-2 and ∫-3-7fxdx=3 find the value of ∫-3-2fx-5 dx

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

A: In any rational function of form p(x)q(x) where p(x),q(x) are polynomials giving real outputs; the…

Q: Which value must you assign to a so that f(x) is continuous at x = 6? 6 + 5x - x? x#6 f(x) = x-6 a x…

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

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].

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