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

Q: Find the x -values (if any) at which f(x) is not continuous, where (x-5

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Q: Describe the interval(s) on which the function f(x) = is continuous.

A: The given function fx=xx2+x+2 is in gxhxform. The numerator gx=x is continuous for all x∈-∞,∞ in its…

Q: Let f be a continuous function such that f(x) dx: = -1 and f(x) dx = = 9. %3D 2 2 | f(x) dæ? What is…

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Q: If f is continuous and f(x) dx = -1, find f(2x) dx.

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Q: Describe the interval(s) on which the function is continuous. f(x) = (x + 1)/√x

A: We can not have negative number inside the square root.  So, x≥0   And we can not have 0 in the…

Q: If f is continuous and f(x) dx = 8, find xf(x?) dx. %3D

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Q: Describe the interval(s) on which the function is continuous.

A: Given: fx=xx+3

Q: f(x)=210, where is it continuous?

A: Given: fx=210 We know that graph of given function is horizontal line for every value of x

Q: Determine if the function f below is continuous at x = 1: [1– VI– x, x 1

A: We have to find

Q: Let f be a continuous function such that -6 [', f(x) dx = 9. What is the value of -3 f(x) dx = -10…

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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: Suppose f" is continuous everywhere. For any constants a and b, show that xf" (x) dx = bf" (b) –…

A: Explained below

Q: 67. If f is continuous and f(x) dx = 10, find f(2x) dx

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Q: Consider the function f(x) : Find the value of B such that (3x + B if x> 3* f(x) is continuous at x…

A: Given: fx=2x2+3  if x≤33x+B   if x&gt;3

Q: Let f and g be continuous functions. If dx = 5 and g(x) dx = 7, then | (3f (x) + g(x)) dx = O 22 -6…

A: As per guidelines we can solve only one question at a time, so the first question can be solved as…

Q: Let f be a continuous function such that f(x) dx = –3 and -8 7 | f(x) dx = -2. What is the value of…

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Q: If f is continuous and f(x)dx=4, | xf(x?)dx=

A: We will find the value of the integral as following.

Q: Let f be a continuous function such that | f(x) da = 13 and 10 3 f(x) dx = 8. What is the value of…

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Q: Determine if the function f(x)= are uniform X continuous on the interval I= [0,1]

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Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

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Q: Suppose that f, g and g' are continuous on the interval I = {x : a <x < b}. Show that f f (x)dg(x)…

A: Given that the functions f,g and g' is a continuous function on the interval defined as  I=x:a≤x≤b…

Q: f(x) = Vx-3

A: Given function is fx=x-3.

Q: Let f be a continuous function such that | f(x) dæ = 5 and f(x) dx = 3. %3D | 4f(æ) dæ? What is the…

A: Recall: Properties of integral:  i)   ∫abf(x)dx=-∫baf(x)dxii) ∫abf(x)dx+∫bcf(x)dx=∫acf(x)dxiii)…

Q: If f is continuous and f(x)dx=4, xf(x2)dx=

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Q: Describe the interval(s) on which the function is continuous.                            f(x) =…

A: fx=xx2+x+2 Since there is no common factors in the numerator and denominator, therefore there is no…

Q: Determine the values of a and b such that the function is continuous on (-00, oo f(x)-ax+b, -l<x<3…

A: We have to find value of a and b so that function is continous is given interval  (-inf,inf)Function…

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: Iff is continuous on [a,b], and f(x) 20 then A True False ر VFX √f(x) dx = dx = √5 F(x f(x) dx

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Q: Let f be a continuous function. Show that 2022 f(x) dx. 2022 dx

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Q: g(x) = sec(x) %3D

A: To find all the intervals the function g(x)=sec(x) is continuous

Q: 9. If f is continuous and f(3x) dx. f(x) dx = 8, evaluate Answer:

A: Given:

Q: Determined where the function f(x) is continuous

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Q: Find the constant a such that the function is continuous on the entire rea 6sin x X g(x) = a 8x if x…

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Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: Let f be a continuous function such that 10 9 f(x) dx = 5. What is the value of f(x) dx = -6 and…

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Q: Let f and g be continuous functions. If Sz f (x) dx = 6 and f g (x) dx = 10, then f3 (5f (x) +g (x))…

A: Use property of definite integration

Q: If f is continuous and f(x)dx = 4, find So xf (x?)dx. %3D

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Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

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Q: If f (x) is continuous on (a,b], we define f (x) dx= lim f (x) dx Xa+ x

A: Solution

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: Assume that f is continuous everywhere and that c is a constant. Show that

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Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (a²² + y² – 4)

A: Given function is                                                              f(x, y)=ln(x2+y2-4)…

Q: Let f be a continuous function such that f (x) dx = -4 and 1 f(x) dx = –14. What is the value of 2…

A: As we know that;  The properties of the definite integral; 1). ∫abfxdx=-∫bafxdx…

Q: Find the number a and b at which f is continuous everywhere? x+a if x 1

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Q: If f is continuous on [a,b], and f(x) > 0 then (A) True B) False √√° √F(x) dx = ₁ √ [F(₂ a - f(x) dx

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Q: Use the definition of continuous to proce whether or not the function is continuous at x=5z (F2, D3)…

A: See the attachment

Q: For all continuous function f: [0, +o] → R, a > 0 we need to prove that 2*f) dx = [ xfw)dx

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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.