13. Find an equation for the tangent plane of the graph of f at the point (xo, yo, f(xo, yo)) for: (a) ƒ: R² → R, (x, y) → x − y + 2, (xo, yo) = (1, 1)

Q: f(x, y) = xy², (3,-2). alru) — sin(ru) (9) T

A:

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A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

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A: Explanation of the answer is as follows

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Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

A:

Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

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Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

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Q: Given the following relation between x and y answer the following questions. a) Using implicit…

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Q: 5. nts) Let F =, use Green's Theorem to evaluate F. dr where the curve C is C the curve shown in the…

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A: Directional derivative

Q: '] Find the derivative of the function. a) y=c sint+\t cos t b) y = secx+e

A: Tje solution of the problem is given in the next steps .

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A:

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

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A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

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A: Given Information:The curve  and the curve  on .To show:The curve  represents a meridian (line of…

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Q: 1. Consider the function f(r, y) = 70 – 4.x2 – y2. (a) Find the tangent plane to f(x, y) at (-3,…

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Q: 1. A function of two variables is given f(x, y) = x² + y² + e-(x² + y²) a) Draw a picture of the…

A: The given function is fx,y=x2+y2+e-x2+y2.   The equation of the tangent plane at a point…