Exercises 1. Integrate each of the following functions with respect to r: (a) rº, (b) r'/2, (c) r3, (d) 1/x*, (e) 4, (f) VI, (g) etz

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A: Differentiation

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Q: If z = x + jy, then O Check whether the function f(z) : 1 is an entire function. State the reasons.…

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Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: 6 Y = x6 + Vx5 ++5 x3 y' = 6x5 +x² – 18x* y' = 6x5 +x1.5 – 18x-2 O Option 2 Option 1 y' = 6x5 +x15 –…

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: , (х, у) (0,0) x+y f(x.y)%3D (х, у) (0,0)

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Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

Q: I need solution please help me.

A: Step 1:To prove that 𝐹(−𝑧)=1−𝐹(𝑧)for 𝑧>0, where 𝐹(𝑧) is the cumulative distribution…

Q: Use implicit differentiation to find dy/dx and d²y/dx². xy + 3 = y, at the point (4, -1) Select one:…

A: According to guidelines I can solve only 1st question

Q: - Find and sketch the domain of the functions: √x+y+1 x-1 b) f(x, y) = x ln(y² - x) c) f(x, y) =…

A: The given functions, a) fx,y=x+y+1x-1b) fx,y=xlny2-xc) fx,y=6-3x-2y We have to find the domain of…

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, −1), u'(3) = (8, 1, 6), and v(t) = (t, t², t³).…

A: The given functions and function values are .The aim is to find the function value .

Q: -1 A = 0 2) 0. x)T. F(e,) = ( 2

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Q: For the function f(x,y) = sin (3x − 7y), find of of dy of af and ?x ду

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Q: Exercise 6: Suppose f and g are functions such that: -3 f = 1, i=7, f = 5, -3 Г» g = 6, g = 3, :-4.…

A: Suppose f and g are functions such that

Q: Find f, (x.y) and f, (x.y) Then, find f, (-4.- 3) and f,(-1,- 2). (x.y) = 2x°y? f(-4,-3)= (Simplify…

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Q: Determine if f(x, y) = xe*-y + 100y is increasing or decreasing at (-2,1) if a) we allow x to vary…

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Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: f:R→Ris a function with an inverse given by f-1(x) = eabx³ _ e- abx?, x €R where B is an unknown but…

A: Given f-1x=eabx3-e-abx3, x∈ℝ with a=-8. ⇒f-1x=e-8bx3-e8bx3. Equating to y and simplifying,…

Q: f(z)=ze^tz/z^2+1 for this function find the Rez(f(z),i) and Rez(f(z),-i) .

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Q: Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

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Q: Let f(x)=(x+4)^3. What are the gradient and equation of the chord/secant between (2,f(2)) and…

A: Given function fx=x+43 The formula for finding the gradient of the chord that passes through 2…

Q: Differentiate the function. (4t + 1)3 (5t – 1)4 F(t) = In F'(t) =

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Q: Find f, and f, and evaluate each at the given point. y' ху f(x, y) = (5, –5) 1. X - y' fa(X, y)…

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Q: Let f : D → E be a function and let A C D, BC E. Prove the following: (a) f(f-1(B)) C B. (b) If f is…

A: The function is f:D→Eand A⊆D and B⊆E