If T:X→X is a contraction for n>1, show that T need not be a contraction

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

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Q: Prove the following Quotient Rule, where f, g are differentiable:

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Q: x(x²+3) Q7. Consider the function f : [0, 1] → R, → √√4+24 Explain why (a) f continuous, (b) f is…

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Q: The function Arg(z) is discontinuous at Select one: O a. {z = x + iy: y = 0, x 0}. * O d. (z = x +…

A: The argument of a complex number is discontinuous at each point on the negative side of the axis. So…

Q: Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some…

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Q: The domain of the function h(t) = vt – 9 is O [9, 00) O R O (-00,9) O (9, 00) O (-∞0,9]|

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Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Let z(x) ~N(0,1) Prop (x > -0.56) = Prop (x ≤ -2.17) = Prop (-1.56 ≤ x ≤ 0.72) =

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Q: Let f(x)= V x³ at the interval of [0,2] ; then , use the mean valune theorem to find c.

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Q: Find the critical points for the function in terms of b: Ax) = 3x-e

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Q: Q4E. f:(0, 19/4] R defined by f(x)=(19–4x). Prove that f is a one to one function mapping onto [0,…

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Q: Let f: X→Y be a function, and let A,BCY. Prove or disprove: f-¹(A)uf-¹(B).

A: The given statement : f-1(A ∪ B) = f-1(A) ∪ f-1(B) is true and we shall prove this statement.

Q: Let f(x) = V5x² – 20. Find everywhere f is continuous. -

A: Given fx=5x2-20

Q: Assume that h: [a, b²] → R is a continuous function and let G : [a, b] → R denote the following…

A: Answer Explanation:

Q: Show that the function f(x): = √/x² is uniformly continuous ON A:= [1,00), but that it is not…

A: To show that f(x) is uniformly continuous on A, we use definition of uniform continuity and to show…

Q: Let fx (x) = x +b, x ∈ [−2b, 2b]. For which b is fX (x) a pdf?

A: Given,  fx (x) = x +b, x ∈ [−2b, 2b] To find the value of b for which fX (x) is a pdf.

Q: Use the linear approximation to approximate a suitable function f(x, y, z) and thereby estimate…

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Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

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Q: Let f(x) = 36 – 5z – z?. (A) Use interval notation to indicate where f(z) is increasing. Note: Use…

A: Answers are provided below.

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

Q: Graph the function h: Z→Z, defined by h(x)=| 3

A: Graph of the function

Q: Ex filnd divergenceof f when yj at (o1). 2 e ( + 9 J

A: See the answer below

Q: Let f(x) = |x|+|x−2], x € R. Find points where f is not differentiable.

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Q: et f(x) = 2x6. Compute = coño + C₁7₁ for the domain

A: Given,          f(x)=2x6 To find:        φ^=c0π0+c1π1 for the domain 0≤x≤1 And  π0=x,   π1=x2

Q: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

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Q: 11. Let f(x, y) = x² - y, g(t) = (Int) In(1-t), and h(x, y) = g(f(x, y)). Find the set on which h is…

A: Given that  f (x, y) = x² - y g(t) = (In t) In(1 - t) We have to find the Composite Function h(x, y)…

Q: f(x) = {*- Įx² +px + 2,x # 3 3, x = 3

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Q: 31. Assume that f is continuous and 2x S f ₁ f(t) d² = 4 + x²" dt (a) Determine f(0). (b) Find the…

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Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

Q: Let f(x)=√x. By use of the little o notation justify that the linear approximation to f at x0…

A: Given,           f(x) =x

Q: Let f(x)=1/x. Show that f is bounded from above on any interval (α,1), where α>0, but the function…

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