k -1 k+1 (',) Let h : Z→ Q x Q. given by h(k) = 2'2 Let G = {(m,m + 1) | m E Z}. Show that G C h(Z). %3D

Q: 40. Let f be the function given by f(x) = -32 +2³ on the closed interval [1,4]. What is the…

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Q: Let F(x) = f(f(x)) and G(x) = (F(æ))² . You also know that f(8) = 4, f(4) = 3, f'(4) = 2, f'(8) = 10…

A: We will differentiate the given functions using the chain rule of differentiation

Q: The graphs of the functions f and g are shown in the figure. y -1 Let u(x) = f(x)g(x) and v(x): =…

A: Given: Let  and To Find:

Q: 14. Consider the function f(x) = xª – 2x?. %3D - a) Find the interval(s) where the function is…

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Q: Let f(x) = cos t dt ,x> 0. Then Ax) has (a) maxima when n = - 2, - 4,- 6, . . . . (b) minima when n…

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Q: • The Range of f (x) = v1-x is 1. [-1, c0) 2. (-0, 1] 3. (-0, 0) 4. [0, 0)

A: Domain: The set of possible values of 'x'                    for which 'f(x)' is defined. Range:…

Q: 3. Determine the function f (x) for which f' (x) r3 II

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Q: 7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te²4), g(t) = (-e“, 1 – t²), for…

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Q: The function z(x, y) obeys, = -2e Which of the follow represents a valid first step for finding u(x,…

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Q: =. Evaluate the following. C. Consider f(x) = 4 – x² , g(x) = Vx +3, h(x) 1. (f° g)(1) 2. (g• h)(1)…

A: Just I have used the definition of composition of two functions, and using given functions calculate…

Q: Consider the three points (2, 4), (4, 6), and (-2,7). (a) Supposed that at (2,4), we know that f₂z =…

A: Let us consider the given function f(x,y) and (a,b) is critical point then fx=fy=0. Determine…

Q: [1, Ost)

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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: let X~N (20,0.36), if P(X<b) then the value of bis = 0.05

A: X~N(20,0.36) Mean(μ)=20 standard deviation(σ)=0.36

Q: L4. A function f is given by sin(yzn) f(x,y,z) = 4x³yz + (3xy²)-1+ (a) If x = 1+, y =-+ z=-1+ %3D…

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Q: ôf Find dx fe for the following dy and x?y (a) ƒ(x,y) = y4 + 3

A: Consider the given function: fx,y=x2yy4+3 Here, the objective is to find the value of ∂f∂x and ∂f∂y

Q: form Demonstrate that the solution of dy = -1 yn+1 for any n = 1, 2, 3, 4, ... is always of the dt 1…

A: Step 1:Solution-True for any n=1,2,3,4---Step 2: Step 3: Step 4:

Q: 4. g(w) = (3w - 2)*(5w – 4)² 5. G(u) = u³(u+ 1)²(u + 2)

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Q: Can you find the values of n and f(t) the given theorem to be used with?

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Q: Write the function in the form y f(u) and u = g(x). Then find as a function of x. dx 8 y = | 4x -X 8…

A: Given :    y = f(u)    u = g(x) y = ( 4x2 - 8/x - x )9

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: (i) If y =g (x1- x2). Let u = x1- x2, show that (a) ay/du = ây/Əxı=- dy/ax2 %3D (b) a@y/ðu² = y/Əx¡²…

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Q: For the function y = f(x) = x² - 2x - 3, x ≥ 1, find (f¹)'(-3)= df 1 dy ly 3

A: We can solve this as follows:

Q: 11. Let f(x, y) = 2x²y. From which of the given (x, y) points does ƒ have the largest direc- tional…

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Q: V Sove using variaton of parameters recuction of order or (D² - 2D+1) y = e*(e*+)*

A: Please find attachment for the details solution