[4.if 0s.r<1 3: Let f (x ):[0,3]¬→R defined by f(x) = 3,if_x=1 nent Show that [5.if 1

Q: {-) Evaluate the domain of f(x)=Ven(Sx-XE)

A: The given function is f(x)=ln5x-x24

Q: If f"(x)>0 on an interval I then...

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Q: Use ƒ' and ƒ" to complete parts (a) and (b).a. Find the intervals on which ƒ is increasing and the…

A: f(x)=xx+9 To find: (a) The intervals on which f is increasing and the intervals on which it is…

Q: Suppose 2 < f'(x) < 6, for –1 < x< 1. Then f(1) – f(-1) is between A) 2 and 10. B) 4 and 12. C) 0…

A: GIVEN : 2 ≤f'(x) ≤6,  for -1 ≤x≤1 TO FIND : f(1) - f(-1) HINT : Mean value theorem

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: A function f has f(25) = 22, f (25) = 2 and f" (x) < 0, for x ≥ 25. Which of the following are…

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Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

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Q: 9. What is the domain of the function f(x) = Vx- 3? | A. (3, 0) B. (-00, 3] С. [3, о) D. (-00, 3)

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Q: 1 is IR? \ {(0,0)}. 22 + y2 The domain of the function f(*, y) True O False

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Q: Ex:- f: [2₂2] →IR xzo f(x) = { } 2 Show that fERE 2, 2] and find S²fdx

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Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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Q: 4. If /(r.y)=- , find f, and f,. V+y

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Q: Let /(x)= and g(x) = 2x. For all x-values, g(x) > f(x). f(x)=()* O True O False

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Q: 5. Let f be defined by the floor function f(x) = [] and let S = {-3, -2, -1, 0, 1, 2, 3}. a)…

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Q: Let /: X→Y be a function, A, B C X and C, DCY. Show that: 3. If CSD then SF (D) 4. f¹(COD)=f-¹(C)…

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Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: 12. Let f(z,y) = < then f(1,2) = (b) 글 (d) 금

A: Given :fx, y=x-yx+y-1

Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Let f(x) = x° – 2, -1< x < 3 The domain ofƒ¯is the interval [A, B]| where A = and B =

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Q: (a) Prove that if æ > 3 and y > 4, then ry > 11. (b) Determine the range of f, if f : D → R, where…

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Q: 1. Suppose that f is a differentiable function and f'(x) ≤ 4 on interval [-5, 2]. If f(2)= 6, then…

A: Suppose that  is a differentiable function and on interval .If , then to determine the smallest…

Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

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Q: 4. Which ones of the following functions are valid CDFs (all have x ≥ 0): (b) 1-exp(-) (0)1-exp(-)…

A: We are given the set of cumulative distribution functions .We have to choose which of the given…

Q: 3. For all x in the interval [2,5], the function f has a negative first derivative and a negative…

A: Answer

Q: VI. Let f(x)=x²-x²-x+1 on [-1,2]. Find all numbers c satisfying the conclusion to the Mean value…

A: Let fx=x3-x2-x+1 on -1, 2.To find all numbers c satisfying the conclusion to the Mean value theorem.…

Q: Determine if the following are analytic or not?

A: Check the function f(z)=eez is analytic.

Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

A: Consider the given information. f"(x) &lt; 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] &lt; favg &lt;…

Q: Let f(x) = ²³ d. Find the value of ƒ¹ (2) af(x) 0 24 4 -8 -4 -24 12 -12 8

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Q: Which of the following statements are true? There can be multiple true statements; indicate all of…

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Q: (b) Determine the range of f, if f :D → R, where f (x) = x?. I. D = (-2, 2) II. D = [-7, 2] III. D =…

A: