Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y², (5, 9, 16)

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Evaluate the integral of: * dx x2 – 2x + 50 arctan (x - 1) + C arcsec (x - 1)/7 + C O 7 arcsin (x -…

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Q: (x – 3y + 3)dx + (3x + y + 9)dy = 0

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Q: Using the table below. Write all the possible idea that you may seen in the graph. (one sided limit,…

A: Given

Q: Find the vector component of v = (4, -1,7) along b = (1, 2, –2) and the vector component of v…

A: The vectors v=4,-1,7 and b=1,2,-2

Q: 12. Solve the initial value problem where v = xex, y(0) : v (0) =- 2: v (0) =- 3.

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Q: Find the directional derivative of f at P in the direction of a. f (x, y, z) = xy + z²; P(3,4,–4); a…

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Q: Solve the following and show the complete solution. 1. Find Duf at P: f(x,y) = sin(8x – 5y); P…

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Q: Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (10, 0) Vg(10, 0) =

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Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: Find the vector component of v = (4, -1,7) along b = (2, 3, –6) and the vector component of v…

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Q: How can you say that S (x² + 5x + C) dx = 3x + 5 is incorrect?

A: Given problem:-

Q: Use the Comparison Test to determine if the series converges or diverges. Sn+ 6n n-1 diverges O…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the ezact answers in terms of i.j…

A: First find the magnitude of the vector and the find unit vector

Q: Find the vector component of v = 2i – j + 3k along b = 3i + 6j + 6k and the vector component of v…

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Q: Find a1 and r for a geometric sequence {a, from the given information. 41 az = 123 and a,= 9 a1 r=

A: The given terms of the geometric sequence,a3=123 and a6=-419

Q: y'sec²xdx – (1– 2y'tanx)dy = 0

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Q: 43. fry(x, y) if = e"* f(x. y) en?

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Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

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Q: Find the derivative of the function. f(u) = u7e−u

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Q: Find the directional derivative of f at Pin the direction of a. f(x, y) = 6x*y²; P(1, 4); a = 12 i –…

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Q: 2y Find the directional derivative of f(x, y, z) = x + z at P(4,4, –3) in the direction from P to…

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Q: Determine if the following statement is true or false. The points P,(2, 0, 1), P2(3, – 2, – 3),…

A: We know that three points P1, P2, P3 lie on the same line if direction ratios of P1P2 and P2P3 are…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: First we find partial derivative with respect to x and y.

Q: 1. State the domain and range of {(x, y)|y = + 3}.

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Q: Determine whether the series converges. Σ Vk+ 3 k=1 The series converges. The series diverges.

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Q: (2x – 3y +1)dx – (3x + 2y – 4)dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: A particle is moving on a straight line has acceleration a=5-3t and it's velocity at time=2. If s(t)…

A: Solution: a = 5-3t v(2)=7 s(2) - s(1)=?

Q: What is the derivative of y = (2x)" O (2x)^(x) (1-In2x) (2x)^(x) (1+2 In2x) (2x)^(x) (1+In2x) O…

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Q: au = 6x + 7, du = e*dx. %3D

A: answer is in next step

Q: x² + y2 + z? = 26, (1, 4, 3) (b) Find a set of symmetric equations for the normal line to the…

A: Let f(x,y,z)=x2+y2+z2-26

Q: Test the series below for convergence using the Ratio Test. 0.7" n=1

A: Given,  ∑n=1∞n40.7n

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) x²…

A: The given curves are y1=x2+2x+5  &  y2=2x+15

Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges giver 1 by the vectors u, v and w…

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Q: Find the directional derivative of f at the point P in the direction of a. i-j f (x, y) = 2x3 – 6y³;…

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x-3y+5z+13=0

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Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: at aw (b) Find at using partial differentiation of the function f(r, s, t, w) from the given…

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Q: s+2 s(s-3) 25 s(s-2)

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Q: y" + 4y' + 6y = 1 + e¬2t , y(0) = 0, y'(0) = 1

A: We need to solve the differential equation.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 6j as…

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Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: Find the solution with the given initial condition. r"(t) = (e', sin (t), cos (f)), r(0) = (1,0, 1),…

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Q: z = 3 - t , z = 6 – 4t parallel.

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Q: Determine if the following statement is true or false. The points P1(12, 9, 9), P2(6, 3, 0), P3(0, –…

A: A detailed solution is given below

Q: x2 1. Let f(x) = 3Vx² – 1 and g(x) x4 – 81 (a) Determine the domain of f and g. (b) Compute gof and…

A: Find domain.  According to guidelines we solve only first question.

Q: Solve the differential equation. dy = 5 ex-y dx

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