3. Describe the interval(s) on which the function is continuous. c) S(x)= x-1 2, x= 1

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

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

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (x² + y² – 4)

A: According to question given thatf(x,y)=ln (x2+y2-4)

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: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

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: Is f(x) = -3 A. Yes B. Does Not Exist continuous at x = 3? C. No D. Cannot be determined

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Q: If functions ƒ(x) and g(x) are continuous for

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Q: Based on your work in part a, on what interval(s) is f(x) continuous?

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Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

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Q: Determine the interval (s) on which the function f(x) = 3xe* is concave down. O 号

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Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: Suppose that f(1) = 3, f(4) = 5, f '(1) = 4, f '(4) = 4, and f " is continuous. Find the value of xf…

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Q: 6. Suppose that ƒ is differentiable on (a,b). interval [a, b]? Justify your response for find a…

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Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

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Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: h(x) = { 3-2 -2 if x≤-1 Cx² + 4x if x>-1

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Q: Prove thait if y=f(x) f(x)=0 when x is a rotional number, then f(x)=0 for all x € R. is continuous…

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Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) >0. Does f have a local…

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Q: 45. For what value of a is x2 - 1, x < 3 2ax, f(x) = %3D 2ах, continuous at every x?

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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: Suppose that f(1) = 2, f(4) = 8, f'(1) = 10, f'(4) = -3, and f" is continuous. Find the 4 value of…

A: We have to find the value of the given integral.

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

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

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

A: From the given problem: 57).   fx=12x+1,x≤23-x,x&gt;2   As we know that, if L.H.L is not equal to…

Q: 2- For what value of the costant c is the function continuous at every number? F(x) = {x+c if x<2…

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Q: Consider the following function: f(x, y) = {xy cosy/3x2 + y2     if (x, y) 6 not equally to (0, 0)…

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Q: What value of c makes the following function continuous at (0, 0)? f(x) = с, x + y² + 5, (x, y) #…

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Q: Use the definition to show that the function f(x) = → is continuous on the interval [c, o), %3D…

A: The given function is f(x)=1x2 .we have to show that f(x) is continuous on the intervel [c,∞)…

Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

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Q: show that f,given by f(x) x +0 )is continuous on R-{0}

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Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: (Read the dėlihition Caleluny.) |x2, if x l; is differentiable at 1. 2x-1, ifx > I; 4. Prove that…

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Q: Suppose that  f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 5, and f ''  is continuous. Find the value of…

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Q: 3. For what value of b, f(x) is continuous at every x? f(x) = {, x -2

A: Given that, fx=x         x&lt;-2bx2      x≥-2

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

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Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: x+ (х,у) # (0,0) f(x,у) — 1-/x² +y² +1 k (х, у)%3 (0,0)

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Q: If f is a continuous function and F'(x)=f(x) for all x € R, then - x)dx=?

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Q: Find the values of the constants a and b, that make (ах + b, ifx3 Both continuous and differentiable…

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Q: Q2 Evaluate whether the function 1-xy if xy # 1 z = x-y if xy = 1 continuous at (1,1) or not.

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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: j(x) = v2x – 4 %3D

A: We have  jx=2x-4   Function is continuous when 2x-4≥02x≥4x≥2

Q: 1. Explain what it intuitively means for function f(x,y) to be continuous in some domain D.

A: To explain the meaning of the given statement.

Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

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Q: Find the value of fa) which makes f(x) continuous at x = a (if exists) where X - x f(x) a =

A: Given function is fx=x-xx Find the value of fa=0.