Find the equations of the normal line and the tangent plane to the parametric surface defined by the vector-valued function R (u, v) =< u² + 1, v² − 1, 2v – u > at (2, 3, 5).

Q: x= x³ = x Find the equilibrium points and their stability in the system

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Q: 9. The explicit formula for the hexagonal numbers is an ¸ = n (2n − 1). Find the 15th and 34th…

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Q: Describe the steps in words that you would use to show that (x-a) is a factor of x" - a". Your…

A: Introduction: A statement P(n), where n is a natural number, is an example. Then, employ the…

Q: 1. X = ¬ [(¬P → Q) ^ ¬(¬P ^ Q)]

A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

Q: (jw+4) (jw+3) (jw+2) B + (jw+3) (jw+2) A(jw+2)+B(jw+3) (jw+3) (jw+2) Ajw+2A+Bjw+3B (jw+3) (jw+2)…

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Q: Find the derivative where w=5xyz, x=2t, y=4t, and z=3t-³. dw 1 dt dw dx (Type an expression using x,…

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Q: Solve the given DE using 3 possible solutions: y' X 3 - 2y 3 3xy 2

A: Given DE  y'=x3-2y33xy2  …………………………(i) we can write it as dydx=x3-2y33xy2

Q: What is the area of the parallelogram formed by the two vectors = (1,5) and 7 = (-3,-2)?

A: We need to find the area of a parallelogram formed by the given two vectors u→=(1, 5), v→=(-3, -2)

Q: A continuous distribution is described as follows: The distribution effectively forms a line…

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Q: the jw2 (jw) ² x 120) = -1.e 20م + 2 + +2+ How did he get the yalue inside the circle ir

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Q: Test the series for convergence or divergence. 8n! n=1 convergent O divergent

A: We use Ratio test of convergence.

Q: Solve y"+8y'+ 20y = 0, with y(0) = 2, y '(0) = -7

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Q: Use the inner product (A,B) = 2a11b11 + a21b21 + a12b12 + 2a22b22 to find (A, B) for 0 A - [27][221]…

A: Given A = 1-124,   B = 01-20

Q: (f) [(3x − 1)√x² + 2xdr

A: Since you have posted multiple questions we have solved first question for you. If you want all…

Q: 8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² − z² = 0 is a point. (b) T F If…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: DUSES 4+ + + x + 8 = 4 X=4 Би мојо! Әч Јәр

A: We have to find the area between y=x2 &amp; y=8+x using graphing utility

Q: Question 2: Tutorial 10 x² and g(x) (b) If f(x) x³ with x € [1,1], find the c € (-1, 1) by using…

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Q: Let S be the transformation whose matrix is A, and let T be the transformation whose matrix is B,…

A: We find required matrix C.

Q: f(x+h)-f(x) for g(x) = 4x²-3x h 5) Find the difference quotient, i

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Q: The annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. Hence the…

A: Firstly annual no of burglaries rose by 50% .

Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

A: (a) Let p be an odd prime. There are p-12 quadratic residues  in ℤp Hence there are total 19-12=9…

Q: If angle D measures 5(8x + 5) degrees, and angle B is 345 degrees, what is ? X =

A: angle D and Angle B are same  therefore  5(8x+5)=345 (8x+5)=345/5 8x+5=69 8x=69-5 8x=64 x=64/8 x=8

Q: For each of the following, either provide all such geometric objects, or explain why none exist. a)…

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Q: Solve the given differential equation by undetermined coefficients. y" + y = 6x sin(x) y(x) = X

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Q: R→T T :. P ¬Q) → (RAS) 1 2 3 4 5 7 8 9 STATEMENT R→ T (¬PV ¬Q) → (RAS) ¬RV¬S ¬¬PV¬Q) REASON…

A: I shall solve in details in next step

Q: JA ITI system is described by the D.E. y +6 Y+8y=2X(t)_ find h(t), then find y(t) if X(t) =…

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Q: Find the critical numbers of the function f(x) = 3x5 + 15x¹ − 25x³ 4 and classify them. At x = At x…

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Q: Find the volume of revolution resulting from the region bounded by 3x-y²+2=0₂ xty = 2, and y = ³√x,…

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Q: Evaluate the iterated integral below. π 1 S*S'y cos (x) dy dx S. 0

A: Here we have to find given iterated integral.

Q: Given y(4) 6y" - 36y" + 216y' = t² - 5 + tsint, determine a suitable form for Y(t) if the method of…

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Q: Find the radius of convergence, R, of the series. xn R = 8 Σ n = 1 I = 1.3.5 (2n-1) Find the…

A: A series ∑n=1∞an will be convergence  If L=limn→∞an+1an&lt;1

Q: [1 0 1/3 0 1 1/3 0 0 1/3 Numerically verify that each initial state vector xo has the given…

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Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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Q: Express the volume of the solid that lies between two cylinders a² + y2 = 1 and ² + y² = 4 and…

A: Consider the given equation of the cylinders, x2+y2=1x2+y2=4 and the paraboloid, z=9-x2-y2. In the…

Q: Compute the gradient of the following function and evaluate it at the given point P.…

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Q: 8 A ITI system is described by the D.E. _Y +6 Y+8y=2X(+) -2t find h(t) then find y(t) if X(t) = te²t…

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Q: Let V = R². For (u₁, U₂), (V₁, V₂) € V and a € R define vector addition by (u₁, ₂) = (v₁, V2) := (U1…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Consider the solid in the first octant which is bounded from above by the paraboloid z=2-x² - y²…

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Q: Find the solution of the given initial value problem: y(4) + 2y"" +y" + 8y′ − 12y = 6 sin(t) +80e¯t;…

A: We use method of undetermined coefficient.

Q: c) x²y" + 5xy + 4y = 0, x > 0, y(1) = 5, y(1) = -9

A: To solve the following problem, we use the couchy homogeneous linear differential equations method.

Q: Problem 2. Put n balls randomly into m boxes, and let § be the number of empty boxes. Calculate…

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Q: Based on the following truth table and logical statement, which answer below is logically equivalent…

A: Introduction: If two expressions have the same truth value for all conceivable combinations of truth…

Q: Take xlt) then x (w) = => x/w) = x(w) = x/w) == s'i ζω Lx W ziot 1.e -jwt -jw مانت e 1 الے لن 1 x…

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Q: Use the method of undetermined coefficients to determine the form of a particular solution for the…

A: We find Yp(x) by using method of undetermined coefficient.

Q: Solution:- Given H(jw) -(4+jw) 6+5jw-w² It Can rewrite as:- (jw+4) 6+ (jw)² + 5jc (jas+ 4) -1 (jw+3)…

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Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: 1. When the function x is of a single variable e.g x= x(t) then the differential is termed (a) First…

A: When x is function of single variable t then differential of x = x(t) is given by  d(x) = d(x(t)).

Q: Find the derivative dw dt 1 where w=5xyz, x=2t, y=4t, and z=3t-³. X=

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Q: u(x, y) = e¯ª (cos x cos y cosh y - sin x sin y sinh y)

A: We have to find the analytic function for which the real part is u(x,y)=e-x(cosx cosy coshy-sinx…

Q: Suppose U = {1, 2, 3, 4, 5, a, b, c) is a universal set with the subset A = {a, b, c, 1, 2, 3, 4).…

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