Let f(x,y)=xe'+ysinx be a function of variables of x and y such that x = uv and y=u² at u=0 and v= 1 is equal to: . Then a. 0 03/2 b. du c. 1 d. None of the above

Q: Exercise 2. Integrate the following functions. 1. S(3x+2)°dz 2. 3.

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Q: Find a and b such that f is differentiable everywhere. 2 cos (r) if r 0 a = b= f(x) = {

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Q: sin t 1 8). du

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Q: 5. Consider the function f(x) = Vx. a. Determine the equation of the line tangent to f at x 4. b.…

A: SOLUTION-

Q: For each of the following functions, find ∂z/∂x and ∂z/∂y. (b) z = x/y2 - y/x2

A: To find ∂z/∂x and ∂z/∂y. (b) z = xy2-yx2

Q: For each of the functions y = f (x) described below,find f (2).

A: f(2)

Q: 2.,3 2) Find fx and fy if f(x, y) = 2x²y³ – 3xy² + 2x² + 3y² + 1

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Q: 1. f (x, y) = x² + y?

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4. y = V6 – 7x

A: Definition used -                         Power rule of derivative -…

Q: 5. Assume that V × F = V × G. What is the most general relationship between F and G ?

A: ∇ x F = ∇x G => ∇ x (F - G) = 0

Q: 41. For ), find all values ofx and y such thatx,y)=0 simultaneously. and yr.y)=0 f(x, y)…

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Q: . Which of the following is a property of the function y = Inx? Bln (") = Inu A. Inuv = vlnu C.lnvu…

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Q: əz If z = f (x, y), find and for the following equation z=-2xy

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Q: Transform the following function into rectangular. Write y as a function of x. x = In t,y = VE,t >1

A: Given,            x=lnt , y=t , t≥1

Q: 7. Which function(s) have/has a zero at x = 2? y = 2* +2 b. y = x² +2 c. y = |x +2| d. y = Vx - 2 a.

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Q: Q2. If w = f(u, v) , u = cosx and v = sinx, show that: (30 Marks) d?w = v? fuu + u² fvv – 2uvfuv –…

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Q: Let P(A) = 0.4 "and " P(AU B) = 0.6. For what value of P(B) are A "and " B are independent?

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