5. If f(x, y) = Find (1 0≤x≤ 1, 0 ≤ y ≤1 otherwise a. P(X > ¹/2/Y < ¹/2) b. P(X>y|Y > ¹/2)

Q: 8. What is the minimum value of the function defined by y = cosx + 4? В. З A. 2 C. 4 D. 5

A: Given- y=cosx+4 To find- The minimum value of the expression.

Q: Given f(x, y) = 50x + 70y − 5x² − 3y² – xy, and evaluate ƒ(10, 7). f(10, 7) =

A: To evaluate f(10,7)

Q: I don't get how y end up equal to 4/rad3

A: The indefinite integration of the function twice has been done to get the required value of f(3)=y.…

Q: 31. Let f be a function whose first derivative is f'(x) = In (x¹ - 2x² +1)+1 on the interval [-2,…

A:

Q: 3. 1 Let f(x, y) = ₁-x²-y² (a) Find a value of c for which there is no level set at f = c. (b) Find…

A:

Q: 6.42. Describe the sets in which the functions below are positive. (a) f(x,y) = 1-x?

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Q: 4. Solve for k s.t. the function is continuous 9 – x2 f(x) = x # -3 x +3

A:

Q: 2. Compute L4, R₁ and T₁ for the function f(x) = 2 on interval [1, 2]. Verify result from question…

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Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

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

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Q: What is the range of the step function? (1, if 0.5 < x < 1.5 f(x) = {2, if 1.5 < x < 2.5 (3, if 2.5…

A: Range of a function is defined as the set of values the function takes for every value of x in its…

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx2(2-x), 0<x <3 0 <x f(x) =-…

A: It is given that, x be the amount of claim with pdf fx = Kx2 2-x,0&lt;x&lt;30,elsewhere

Q: The function f(x) is continuous and differentiable on the interval [−2,6]. It is known that f(−2)=4…

A:

Q: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

A:

Q: 9. f(x,y) Use the D-test to find all relative extreme values for the function: 2x² + 3y² + 2xy + 4x…

A:

Q: 1.) Suppose a differentiable function has values given by the following table : 1.5 .5 6. 1 8 2.5 25…

A: Consider the given table of values of x and fx. We have to find the most reasonable estimate for…

Q: 13. Explain why f(x) = X - does not have an extreme value on the interval [0, 5]. x-1

A: We have to prove function f(x) does not have extreme value on the interval [0, 5]

Q: y² + 1/²2-44 = = =-=-66 et +2 a) y (-1.5) = 1.7 b) y (8)= -3.14 determine the largest interval a…

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Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

A:

Q: Evaluate f(1) dz, where S7a, 0<<1 f(z) = 4x2, 1<< 2. f(z) dr =

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Q: 3 4/3 Find the length of the curve y = x 3 2/3 8x +5 for 1 ≤x≤27.

A:

Q: 4 and a = 6. 3 Find (f)'(a) for the function f (x) = x²

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Q: 10. (True/False) For any continuous function f(x, y), we have fry = fyr.

A:

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: If f" CQ) = xa (x+)S (x-!) And all inflection points.

A: I have appended the concept used in the solution part

Q: 5. f(x) is defined as f(x) = -3x + A I≤1 r²+(x-1)B-3 r>1 A For what values of the constants A and B…

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Q: ( 2,b,4)' and ||x||,=v/21 then the vale of b = 0 Select one: O True False

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Q: (x+b, x≤1 16. f(x) = ax², x>1' Let f is the function given above. What are all the values of a and b…

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Q: Find all point(s) of inflection, if any, of the graph of the function f(x) =x* – 2x'. с. (-1, 3) а.…

A: