. Determine the value of c such that the function remains continuous. Draw your resulting function to ensure it is continuous Sa² + 1, r>c f(x) | 2.x,

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Q: Suppose that f( is a continuous function. If f(#) da=4, then what is the value of T - f(x)] dæ ?…

A: To evaluate the given definite integral.

Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

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Q: If f(x) is continuous on the interval [a, b] and a <c < b, | f(x) dæ is equal to then

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Q: For what value of c is the function defined below continuous on (-o, o)? – c², f(x) = { x - c², x<…

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Q: If f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) 3, and f"(x) is continuous, what is x f"(x) dx? %3D

A: Given: f(1)=2f(4)=7f'(1)=5f'(4)=3I=∫14xf''(x)dx=?

Q: For what value of b is

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Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

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

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Q: For what value of b is X - b b + l' x 0 continuous at every x?

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Q: 3. Use the definition to show that the function f(x) = is continuous on the interval [c, o0), where…

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Q: c =

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Q: Let f be a continuous function such that 5 √ (f(x) — 2) dx? What is the value of f(x) dx = -2 and…

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Q: For what values of b is - b b + 1' g(x) x? + b, x > 0 continuous at every x?

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Q: At what points is the given function continuous? f(x, y) = V9x + 6y O All (x, y) such that x + y 2 0…

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Q: If f: X →Y is continuous and E C Y is closed, then f-(E) must be: - Closed Open None of these

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Q: For what value of b is             continuous at every x?

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A: We will check the continuity of the function

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Q: For what values of a is Ja'x – 2a, x 2 2 f(x) : \ 12, x < 2 continuous at every x?

A: Given function is Since f(x) is continuous for every x. So, f(x) is continuous at x=2.

Q: Consider the piecewise-defined function Vx+ 1, x> 3; f(x) = { 2b, X = 3; x < 3. %3D ax + b, Supposef…

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Q: 35. Given that f(z) is a continuous even function, then A 0 B D

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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: Suppose f and g are continuous functions on the interval [a, b], then SEAFX) – g(x)) dx = [." f(x)dx…

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Q: Given a set E c (0,1) of measure 0, construct a continuous non-decreasing function f : [0, 1] → R…

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Q: (a) Prove that if m ₹ N, then the function f(x) = xm is continuous on R.

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Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: f (x) = v2 – x at x = 1

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Q: Find the value of a so that the function is continuous everywhere x2 + ax – 2, x 1 O 1 O 2 O 3 O 4 O…

A: Given:   f(x) = x2+ ax - 2  when x≤ 1     f(x) = x + 3 when x &gt; 1

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

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Q: consider a function f:lo 11-» R. and etheruoise iff RELmaan amntegrable DY not A=3+1

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Q: (e) If f(x) is continuous at x = 0, then what is the value of n: if 20 if x=0 f(x)=\ 38

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Q: - For what value of b is Sx, bx?, x2 -2 x<-2 х, g(x) = continuous at every x?

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

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

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Q: øz (@) is a continuous function of o in the range -o < @< ∞.

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Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

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Q: Find the value k that makes the function continuous. S ka?, f (æ) = x > 2 ka + 4, г 2

A: Given thatfx=kx2         x&gt;2kx+4    x≤2We have to find value of K for which function is…

Q: For what value of a is the function continuous at every x?

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Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5