Find the equation of the plane tangent to the following surface at the given points. x² + y²-z²-12=0; (6,1,5) and (-1,-6,5)

Q: 5|2 X 1 If f(x) = X A. f(x) is continuous at x = 2 B. f(x) is discontinuous at x = 2 C. lim f(x) = 1…

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Q: Distance Between Two Cars A car leaves an intersection traveling east. Its position t sec later is…

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Q: If f(x) is linear, g(x) is linear, and h(x) = f(x)/g(x) What is the maximum number of vertical…

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Q: 04:B/ Simplify Moivre's theorem? [cos 30+ i sin30 15[cos 0-i sine 1³ [cos 50+ i sin50][cos 20-i…

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Q: b. ·(b³ + a³) units³ 3 d. -b³ + a³) units³ 16. The arc length is defined as if y=f(x) is a smooth…

A: We have to find the arc length of the curve y=f(x).   According to guide line we solve only one…

Q: Q4 Solve by Gaussian elimination x-4y-2z = 21 2x+y + 2z = 3 3x+2y-z = -2

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Q: Alternative Formula for the Derivative f'(x) = lim Z-X f(z) = f(x) Z - X

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Q: Consider the level surface defined by the equation x² + 2y²-3z² - xyz = 8, find the following: a)…

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Q: Sketch each of the following: . the solid E • the projection of E onto the xy-plane the projection…

A: answer is in next step.

Q: Find the solution of the given initial value problem in explicit form 1 y' = (1 - 5x)y², y(0) = 9

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Q: Q4:B/Simplify Moivre's theorem? [cos 30+ i sin30 15 [cos 0-i sine 1³ [cos 50+ i sin50 ] [cos 20-i…

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Q: Q1: Find the general solution of the following first order D.Es? (Answer two only) CELE MAI ) c)…

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Q: Find the solution of each of the following differential equations: a) y'=ye² +2e¹, y(1) = 3 b) 2…

A: I am attaching image so that you understand each and every step.

Q: Find the solution of the given initial value problem in explicit form. 1 y′ = (1 — 13x)y², y(0) = 6…

A: We can solve the given initial differential equation .

Q: * Parallel lines have the slope (m1x m2 )= -1 true False O

A: Given question:- Parallel lines have the slope (m1xm2) = -1

Q: 11. A hockey player, on left defense, is about to take a shot on net. The net is 1.83m wide. The…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1. S x4+a4 dx x3 2. Jydy √a2-y2 3. I cos2tdt (1+sin2t)4 4. I tanßsec2ßdß 5. [(tan) – 1)2d0

A: We have to find  the value of given intregation.

Q: The following chart shows "living wage" jobs in Rochester per 1000 working age adults over a 5 year…

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Q: 3 4 Q4) Suppose a class contains girls, and boys. Suppose that 40% of the girls have long hair, and…

A: Above question is solved.

Q: xy lim (x,y)->(0,0) x² + y²

A: We need to write down that the limit exist or not.

Q: MTI THE - T C₂ b

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Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. 2t r(t) =…

A: In this question, we want to find the tangent unit vector of r(t) at t=0.

Q: Calculate the work (in joules) required to pump all water out of a full tank. Water exits here. d b…

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Q: Find f'(x) for the following function. Then find f'(8), f'(0), and f'(-9). f(x) = − 7x² + 10x

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Q: -2 2 о 0 Ау N Х

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Q: 16. A cup like object is made by rotating the area between y = 2x² and y = x+1 with x> 0 around the…

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Q: Solve the following system of linear equations: X₂-5x₂+x3 = 2 If the system has infinitely many…

A: The given system of equations,        x1-5x2+x3=2

Q: Find the solution of the given initial value problem. ㅠ ty' + 2y = sint, y (-) - = 5, t > 0 Y ||

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Q: 6 6 Suppose ff(x) dx = −4 and g(x) d -4 3 3 6 Evaluate (3 f(x) — 3 g(x)) dx. 3 Remember to include a…

A: Given that ∫36f(x)dx=-4   and ∫36g(x)dx=-3 we have to calculate , ∫363fx-3gxdx. To solve this…

Q: For the vectors u = (3, 2, 1) and v = (1, 2, 0), evaluate the following expressions. a. 2u+ 4v b. 4u…

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Q: 17. A spring has a natural length of 20 cm. A 40 N force is required to stretch (and hold the…

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Q: Calculus I Consider the following tables

A: We have to solve given Questions.

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: Using the definition of derivative that incorporates the idea of limit, prove that if f and g are…

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Q: Use the Chain Rule to differentiate the following function. f(x) = (3x² + (4x-5)4)7 f'(x) =

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Q: Suppose fe Cla, b] and f'(x) exists on (a, b). Show that if f'(x) #0 for all x in (a, b), then there…

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Q: Differentiate the function. (2x+5) y= (5x+1) 3 기 dx 11

A: Given:       y=2x+545x+13 differentiating with respect to x Apply the quotient rule:…

Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

A: This question is related to vector integration ,we will solve it using given information.

Q: Answer true or false? A function is not a function but is defined on a function space true Ofalse

A: Solution )  a function defined on the function space  Function space is set of function between 2…

Q: Solutions converge to the function y =

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Q: Distance Between Two Ships Two ships leave the same port at noon. Ship A sails north at 12 mph, and…

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Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: If z = y¹ - 4y³ + 4y² - 1, then the set of values of y for which z' equals 0 is A. {0, 1, 2} B.…

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Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

A: I am attaching image so that you understand each and every step.

Q: Find the domain of the following vector-valued function. r(t) = sin 5ti + ²√² + ¹ k e

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Q: 3) √ √6x-x² dx a) 12 (x-3) √ 6x-x² + 2 arcain 2/ arcain X=² X-3 te 3 (x+3) Gx-x2+gain x3tc 3 c) —…

A: solution

Q: Use calculus to find the open intervals on which the function f(x) = x+8√√/2 − x is increasing or…

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Q: Solve the given differential equation by separation of variables. dx + exdy = 0 y = 14e - 4x + C X

A: We can solve the given differential equation by using the variable separable method

Q: itial condition that the point (0, √2 + 1) is on the

A: We have to choose the correct option from the given options according to the given information