Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE: Enter the exact answer. Distance=

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: 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 distance between the skew lines: x = 9+ 6t, y = 5 + 6t, z = 7 – 6t y = 7, x = 7 – t, z = 6…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y2,…

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Q: Use vectors to find the lengths of the diago that has i + j and i- 22j as adjacent sides. NOTE:…

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Q: Determine the folowing integrais: 32+8 1.1 4x+6 1.2 +3r-10 1.3 se (sin Sx)cos Sx dr

A: In this question we have to find the Integration. Note: As per our policy we are suppose to do only…

Q: Calculate r' (t) and T(t) and evaluate T(1). r(t) = (6+ 71,1,5 – 1²) (Give your answers using…

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Q: 3. Prove the following using the epsilon-delta definition of a lir a. lim (2x – 1) = 3 x→2

A: We will prove the limit using definition.

Q: Find parametric equations of the line through (-1,0,3) that is parallel to 5i – 6j+k. x(t) y(t) =…

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Q: = -14 – 5t = -5t y = 21 + 3t = 5t – 43 Given the skew lines l1 : Y = 9 – t and l2 : = 2t – 7 (a)…

A: Since, you have ask a question with multiple sup-parts, as per company guidelines we will solve the…

Q: For the function h whose graph is given, state the value of each quantity, if it exists. (If an…

A: (a)limx→-3-h(x) =4(b)limx→-3+h(x)=4(c)limx→-3 h(x) =4(d)h(-3) = DNE(e)limx→0-…

Q: dx =+c 6. 2.

A: We can solve the given problem as follows:

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (2, 3)…

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Q: Activity 2: Name Me in Three Ways! Directions: Determine if the given function is continuous or not.…

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Q: Express the given parametric equations of a line using bracket notation and also using i. j.k…

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Q: DIFFERENTIAL EQUATIONS Solve the following application problems. *show the every details of your…

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

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Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

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Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

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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: During the summer months Terry makes and sells necklaces on the beach. Last summer she sold the…

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Q: Use spherical coordinates to show that the volume of a sphere of radius R is V = *nR³.

A: Given the radius of sphere is =R  Then equation  of sphere is                      X2 + Y2 + Z2 = R2…

Q: If F(u,v) = (u-v) / (u+v), Find r(금금)+ F(x)

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Q: Find the area of the triangle with vertices P(1, 3, –3), Q(0,0, 0) and R(4, 5, 1). NOTE: Enter the…

A: Here, PQ=Q-P=0,0,0-1,3,-3=-1,-3,3PR=R-P=4,5,1-1,3,-3=3,2,4

Q: Question A tank is shaped like an upside-down square pyramid, with base of 2 m by 2 m and a height…

A: The volume of square pyramid with side of base a and height h is given by, V=13a2h At any height the…

Q: Reindex the series to start at k = 0 y = E, (k+ 1)æ*+3 = E£o

A: The given series is y=∑k=7∞k+1xk+3 we have to re index the series to start at k=0. Rewrite the given…

Q: Find the derivative of the function described. (Rx5) 1. y = (2x + 3) (5x – 4)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Display all powers of 2 that are less than 20000. Display the list in a properly formatted manner,…

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

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Q: •A savaic has propossitien is a ? what is the Mimerical coefficient of -5xy^2? Simplify…

A: The answers are :

Q: Let a = ci +j and b = 7i + 28j. Find c so that a and b are orthogonal. c =

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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: 4. By using Taylor series, show that e* =cosx+i.sin x.

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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(-3,3,1);…

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Q: 4. Given function f (x,y)=e-(x° +y"), and classify them into maxima, minima and saddles. then find…

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Q: Find an equation of the plane through (– 1, 3, –4) that is perpendicular to the planes 8x – y + z =…

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Q: Find the derivative of the function described. (Rx5) 1. у %3D (2х + 3) (5х — 4) y = | Зх-1 2. f (x)…

A: Let's find.

Q: 12. 5 In(3x) dx 5ln (3x) + C 4

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Q: Use the Root Test to determine if the series converges or diverges In n n 9n-10 n-1

A: We can solve this as follows:

Q: 4. x - 3

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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: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

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Q: Let a = ci +jand b = 12i + 9j. Find cso that the angle between a and bis 6' Round your answers to…

A: Solve by dot product

Q: Note the word curve is used to indicate a graph and can be for example a straight line, parabola…

A: We have to find the area enclosed by the curves.

Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

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

A: Given,  ∑n=1∞n40.7n

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v…

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Q: 3. Given below is a table of values of a function Write the limit of a function by concluding using…

A: Function table values are given, we have to find the limit using table values.

Q: A Use the method of Lagrange multipliers in Problems 7-10. I SL.

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