Let r(t) (t¹ + 4, t² + 2t¹, − 4t³). Find the line (L) tangent to r(t) at the point (20, 36, 32) = L: (x, y, z) = +t

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: Show that r1(t) and r2(t) define the same line, wherer1(t) = t (2, 1, 3), r2(t) = (−6, −3, −9) + t…

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Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

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Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0…

Q: -2+z) ds over t e point (0, 0, 0)

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Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

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Q: F=(x-y², x²•y +3) at A-(1, 1), B=(2, –1) and C=(0,-2). %3D

A: The divergence of a vector field F = <P,Q> is defined as the partial derivative of P with…

Q: Let z = (1+z)√√/50 — x² − y². - (A) Calculate the equation of the tangent plane at x = 3, y = 4. (B)…

A: z = (1 + x)50 - x2 - y2 The given function is of the form z = f(x) To calculate the equation of the…

Q: The temperature is T(x, y) = (x-1)² + y² degrees at any point (x, y) on a triangular metal plate…

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: Assume that y is a function of x. Find (d2y)/(dx2) for x2y-y2-2(sqrt x)+4=0 at point (1,2) 7/6 8/6…

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Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: Determine the magnitude and direction of the largest change 2 2 (x² + y²)z at the point M (1, -2,1).…

A: Introduction How sharply a curve rises determines its magnitude. It is simplest just examine the…

Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

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Q: Given the function z = In(x - 2y), find the equation of the tangent plane when (x, y) = (3, 1) in…

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Q: Find the analytic function if the imaginary part is (2xy + 5y) where u (0,0) = 0

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Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…