1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i) =2 BE CONTINUOUS IN == 1-i.

Q: Consider the function if a<0 2 + I if0<I < c, g(x) = if a c where c is a positive constant. Show…

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Q: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). Which of the…

A: Given: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). To Find:…

Q: 34) If f is an even function that is continuous on [-1,3] and if f f(t)dt f₁f(t)dt = 8, then f…

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Q: Verify the Rolle's Theorem for the function (x2-1)(x-2) on [-1,2] find the point in the interval…

A: Given function is : fx=x2-1x-2 To verify the Rolle's Theorem and find the point in the interval…

Q: Let ƒ(x), g(x) be two continuously differentiable functions satisfying the relationships ƒ′(x) =…

A: Given,

Q: Let f [0, 2] → R be a continuous function, with ƒ(0) ≤ f(1) ≤ f(2). Show that there : exists xo [0,…

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Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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Q: If f has a finite third derivative f ’‘’ in [a, b] and f(a) = f‘(a) = f(b) = f’(b) = 0, then there…

A:

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

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Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Verify the Rolle's theorem for the function (x² – 1)(x – 2) on [-1,2] Find the point in the interval…

A: We can use application of derivative in order to solve the given problem.

Q: Theorem 11. Let f be a continuous function on R such that f(x+y)3Df(x)+f) x, yER. Show that f(x)3Dcx…

A: Since you have posted a multiple questions. So,  we will solve only first question  for you. To get…

Q: 10, Let f be the function defined by the following. sin x, x<0 x. Osx<1 S(x)={ 2-x, x-3, x22 For…

A: Given: the function f defined by the following             fx=sin…

Q: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

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Q: Determine the values of a and b such that the function (x -a ,x 1 Is continuous of all values of x.

A:

Q: f(ix, λγ) - λκ. f(x, y)

A: Given: fλx,λy=λkfx,y

Q: • Use the IVP to prove that r3 – 4z+2 has a zero in the interval [0, 1] • Use the IVP (and a similar…

A:

Q: 1. Find if the function is continuous in the given points A) f(x, y) = B) f(x, y) = xy √x² + y² 0…

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Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

A:

Q: Determine whether the functions are linearly dependent or linearly independent on the specified…

A: To check the linear dependence/independence of such functions, the concept of Wronskian can be used:…

Q: 1. Let f be defined on an open interval (a, b) and assume that f has a local maximum or a local…

A:

Q: Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)-f(x) f(y) ♥x, yER. Show…

A:

Q: (1) Suppose f: [a,b] → [a,b] is a continuous function. Prove that there exists a cE [a, b] such that…

A:

Q: Verify the Rolle's Theorem for the function (x2 – 1)(x – 2) on [-1,2] find the point in the interval…

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Theorem 12. Let f be a non-zero continuous function on R such that f(x+y)=f(x) f(y) ¥x, yER. Show…

A:

Q: (1.1) Define clearly what is meant by saying that a function z = f(x,y) is continuous at a point (a,…

A: Function is continuous at a point means "the function is continuous only at one point " The function…

Q: Consider the following piecewise defined function: sin(ax) -1 < x < 0 4x f(x) = a2 –(b+1)x+b x²+x-2…

A: Given function is f(x)=sin(ax)4x,-1≤x&lt;0x2-(b+1)x+bx2+x-2,0≤x&lt;1x2-1+a ,1≤x≤2…

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

A:

Q: A function f: Z x Z is defined as f(m, n) = 3n - 4m.  Verify whether this function is injective and…

A: f: Z x Z is defined as f(m, n) = 3n - 4m So, f(m, n) = f(a, b) implies, 3n - 4m = 3b - 4a i.e. 3(n…

Q: b. Test the continuity of the following function 1, x< 0 V1-x, 0sxs1 ,atx 0,1 x- 2, x21

A: We have to check the continuity of f(x) at x=0, 1

Q: 3. (2') Let A+ cos x x 2. Given that q(x) is a continuous function, determine the value of A and B.

A:

Q: 7. Suppose f is a continuous function on [a, b] and Sf(x)g(x) dx =0 for every continuous function g.…

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Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: Suppose that f and g are both continuous functions. Also f, g € [a, b] and that f= fg. Prove that 3c…

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Q: Find values of the constants k and m, if possible, that will make the function f continuous…

A: If f is continuous at x=a then limx→a-fx=limx→a+fx=fa . Assume , f is continuous every where to find…

Q: 6. Let f be a continuous function on [0, 2] whose second derivative exists on (0, 2). Assume f(0) =…

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Q: 4. If continuous function f:[0,1] U (2,3) → R is one-to-one, is f also continuous? 1

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Q: Let f(x) = 2x+1, if x1 O (-∞, 1) U (1,00) O (-∞0, 1] U (1, ∞0) OR O (-∞0, 1) U [1,00)

A: topic- limits and continuity

Q: Determine whether the given set of functions are linearly independent or linearly dependent on the…

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Q: (c) Suppose that f : [-1,1] →R is a continuous function such that r²+ f(x)² = 1 for every rE[-1, 1].…

A: Given that the domain of the given function is [-1, 1] and function is defined as: f:−1,1→ℝ​is a…

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

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: 3. (10 points) Determine the value of C such that if r +0 f(r) := V16 + 3x – 4 if r = 0 will be a…

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Q: Determine the value of m such that the function 5 + 5 y fi^ - ^ - f(z, y) = is continuous at (0,0).

A: Given that function s continuous at (0,0). We need to find the value of m.

Q: (3x² -1, x 1, Determine c and d so that f(x) is continuous everywhere.

A:

Q: Suppose f(x) = 2=*_ 3z-2 Which piecewise function redefines f(x) as a continuous function? %3D I-2…

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Q: 3. Show that there does not exist a non-constant continuous function f : R2 → R such that f(x, y) =…

A: Given:- f: R2→R

Q: 1-x², x 2 at x = 2.

A: Given, fx=1-12x2, x&lt;23,    x=2x-2-1,   x&gt;2