Suppose: w = f (s,t) s = s (x, y) t = t (x, z) Ultimately, after substituting in the lower variables, w will be a function of x, y, and z. Suppose s (3, 2) = 6 and t (3, 1) = -9. Write down the Multivariable Chain Rule formula for: We (3, 2, 1) =??? [Use Lagrange notation (the subscripts!).] %3D Hint: Where do we evaluate each partial derivative?

Q: Estimate f(1.08, 5.94) assuming that S(1,6) = 4, S«(1,6) = 0.5, S,(1,6) = –0.4 (Use decimal…

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Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Find the domain and range of the function.

A: Given : The function f(x, y) = ln(xy - 6)   To find the domain and range of the function.

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Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. У(х) %3D…

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Q: Ət A. Use the chain rule to find and as functions of x, y, s and t. Ət = მა Suppose z = = B. Find…

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Q: Compute gxxyz for g(x, y, z) = x²y³ z³. (Use symbolic notation and fractions where needed.) gxxyz =

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

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Q: Find the Re

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Q: Find and sketch the domain for the following function: g(x, y) = x-y

A: The given function gx, y=4-x2-4y2x-y. We have to find its domain and sketch its graph.

Q: A. Verify Clairaut's Theorem for the given function: F(U,W) = Sin(UW)- 4U?w2 %3!

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Q: of For the function f(x.y) = In (x + 6y), find- of and dy

A: It is partial derivative so when we differentiate with respect to one variable consider other…

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Q: Assume that a manufacturer has productivity function P(l, c) where I and c are the amounts of labor…

A: given  productivity function=p(l,c) l=amount of labor and  c=amount of capital utilized

Q: Find all relations from S= {1,2} to T = {4,5} Find all functions from R = {2,3} to S = {4,5}.

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Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

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Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

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Q: If z is implicitly defined as a function of x and y via the equation e² = xyz, compute 33 and 3.

A: The given equation is, ez=xyz. To find: ∂z∂x,∂z∂y. To compute ∂z∂x,∂z∂y : Partially differentiate…

Q: Show that f is linear of slope m if and only iff(x + h) - f(x) = mh (for all x and h)

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Q: Let T: P, → R? be the function defined by the formula T(p(x)) = (p(0), p(1)). Find T(5,4). Select…

A: We will assume a linear polynomial whose image is given to us. Now we will use the definition of T…

Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x>0, r>0, λ>0 Y~Gammas,λ fy=λsΓse-λyys-1,     y>0,…

Q: 1, cosX, cos 2X,--- , cos mx

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Q: Let f(¹) = √2 +2. Since f(x) is differentiable on [-2, 7], by the Mean Value Theorem, we know there…

A: Mean value theorem (MVT) If  f(x) is a real valued function in the interval [a,b] which satisfies…