(2x- 3, x<3 10. Given f (x)={3, X =3 0.5x2-x+7.5, x>3 Use the definition to determine if f is continuous at X =3.0

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: 3. If f is continuous and f (x) dx = 8, show that the graph of ƒ intersects the line y = 4 at least…

A: The function f is continuous. The integral function is ∫13fxdx=8.

Q: 1) Find the value of C that make the function continuous at x-1? x 1 -

A: We have given piecewise function  Function is continuous at x=1 if  f1+=f1=f1- f(x) = C-x        if…

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the…

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at…

Q: [2-x², x20 Given f(x) = , find the value c so that f(x) will be continuous at all values. x<0 x +C

A: Given that: f(x)=2-x2,    x≥0x+c,      x&lt;0   NOTE: As per our answering guidelines, we can only…

Q: For what value of b, f(x) is continuous at every x? (a²x-2a f(x) = (12 x2 2 x< 2

A: As f(x) has two parts and both parts are continuous in given x so make continuous only at point x= 2

Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

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Q: Find the value a that will make f(x)={2x^2-7x+3/x-3  if x is not equal to 3…

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Q: On what domain is the function f(x) = – 4+ V3x – 6 continuous? %3D

A: The function is a square root function and hence, the function is continuous in the domain.

Q: Find a value of a so that f is continuous at c = -3, or indicate this is impossible. x+3 x -3 f(x) =…

A: Given the function   f(x) = x+3-5x+3,  x≠-3a,                 x =-3   We need to find the value a…

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx? + 2x if x < 3 f(x) = {…

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Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: 81 xf(x²) dx. 6. If f is continuous and f(x) dx = 4, find

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Q: 3. Find the constant k that will make f continuous on (-0o, 00). Sx – 4 , (kx2 – 24x + 46, x > 5 x<5…

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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: For what values of a and b is -2, xS-1 f(x) = ax - b, -1 <x<1 3, continuous at every x?

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Q: x2 – 4x + 3 - f(æ) = 5. Let x - 3 How could we define f(3) x = 3? so that J is continuous at

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Q: For what value of the constant c is the function f continuous on (-, o)? cx2 + 8x if x 3 C =

A:

Q: If f is continuousand ∫31f(x) dx=8, show that f takes on the value 4 at least once on the interval…

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Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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Q: For what value of the constant c is the function f continuous on the interval (-0,00). f(x)={ cx+1 ,…

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Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

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Q: Evaluate f (x): at x = -2. %D 1 - x2 Select one: A. Discontinuous B. Continuous

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Q: For all but two choices of a, the function (x) x if x a will be discontinuous at the point x = a.…

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Q: f(x) = Vx-3

A: Given function is fx=x-3.

Q: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

A:

Q: Consider the following. S-3x, f(x)={2 - 2x+ 9, x > 2 Find the x-value at which f is not continuous.…

A: We will find the value of x at which the f is not continuous and whether the discontinuity is…

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

A:

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

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: Find the interval(s) where f(x)= x²- 2x+3 is continuous.

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Q: For what value of the constant c is the function f continuous on (-, 0)? S cx2 + 5x x3 – cx if x 4

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Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: Find the absolute extrema of f (x) = x-12x on the closed interval [0, 4].

A: The given function is, fx=x3-12x The interval is 0, 4

Q: 4. For each part, find a real value c that makes f continuous at x=0, if possible. If not possible,…

A: A function is continious , when at that point limit of the function exists , and thatlimit is equal…

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

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Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

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Q: 2. Find the (exact) values of a and b so that f is continuous at a = 2. 8r2 + 20x + 28 if x 2

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Q: f(x) = x² – 3x – 10 %3D

A: The limit of a function at a point is the value of the function when the value of the variable is…

Q: Suppose that f (x) is a continuous function. 3 If | f(x) dx=5, then what is the value of z - f(x)]…

A: Given, ∫13f(x) dx =5Now,∫13[x -f(x)] dx= ∫13x dx -∫13f(x) dx =x2213 -5…

Q: Determine the interval(s) where f(x)-In (5x+10) is continuous. It is continuous in the interval

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Q: (b) FIND the value of c, so that f(x) = {cx – 1, x< 0 lx² – 1. x 2 0 is continuous everywhere.

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Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2