Sketch the level curves f(x,y) = C' of the function f (x, y) = xª – x² + y², for several different values of C E R. In particular, the case C = 0 yields the lemniscate of Gerono. Find the set of points at which the implicit function theorem does not apply to the equation f(x, y) = C to yield y = y(x).

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

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Q: . Sketch the level curves of the function f(x, y) = x² + 2x + y² – 6y corresponding to the z-values…

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Q: Find y as a function of t if y(0) = 5, y(0) = 3. y(t) = 36y" - 84y +58y = 0₂

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.