[2 1 1 V2 = 3 1 V4 1 Let Vj = , V3 1 4 1 2 8 For what value of t is the set {v1, V2, V3, V4} NOT a basis for R*?

Q: Consider the function g(x, y) = x³ – 4x + ye" – In y. a. Find all critical points of g. At each…

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Q: IV. Determine if the given is convergent or divergent. sin(2 tan¬1 n – 1) #3. )) (2 tan-1 n – T) n=1

A: Given series is ∑n=1∞sin(2tan-1n-π)(2tan-1n-π)

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A: B is not the ancestor of J so first option incorrect C is the child of B therefore the second option…

Q: whose Hw.4 theights are de fined by ECXgy) and bases are the regions bounded by the fottowing fin…

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Q: uate the integral fdy dx using polar coordinate

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: To convert into polar coordinates.

Q: [1 1] a Let A 2 1. Find a QR-factorization of A. If R = then the 1 3. value of a is , the value of b…

A: We can solve this using given information

Q: п(x — 2)" 3" (2n – 1)3 * VI. Consider the power series - n=1 a. Show that the power series converges…

A: Given series is ∑n=1∞n(x-2)n3n(2n-1)3

Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of the functions f(x, y) =…

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Q: Refer to the System of Linear Equations below. 4x1- X2- X3 = 3 -2x +6x2 +x3=9 X1 +X2 +7xg = -6 Using…

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Q: (b) If the power series An(x + 1)" converges at x = 2, then >(-1)"an converges. n=1 n=1

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Q: Given the matrix G -K and de = Then do and d, are G - conjugate if d, is given by Non of these

A: We know that,  Two vectors u, v in Rn are A-Conjugate for a matrix A of size n×n if  uTAv = 0  (Here…

Q: Q3) Evaluate triple integral dz dx dy.

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Q: Find whether the shown expression below diverges or converges Show your solution and how you came up…

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Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: for x 1 X, Consider f (x) (2 х, These following statements are true for f (x), except.... jika x 1…

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Q: 2. Find the area of the region bounded byx = 4y – yʻ, and x =y. -2+ 15 A) square units 2 C) square…

A: The area under the curve is obtained by using double integration I=∫ab∫f(x)g(x)dydx or…

Q: Set up but do not solve an integral to find the volume. The base of a solid is the region enclosed…

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Q: Consider the probability density function if x 5. Find the median (accurate to 4 decimal places).…

A: Given PDF is f(x) = 14exifx<034cos(x)if0≤x≤π20ifx > π2

Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of the functions f(x, y) =…

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Q: 4 - 2v2. R

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Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u eR…

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Q: What is the future value if $8500 is invested for 11 years at 12% compounded semiannually? (Round…

A: Given Principal Amount = P = $8500 Time = t = 11 years Interest rate = 12% compounded semiannually.

Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: Q2) Solve the D.E xdy + (2y-x* + 3x)dx 0

A: To solve the given differential equation.

Q: Determine whether the following series is convergent or divergent 3- Vn (a) Vn3 n=1

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Q: Given the power series: +00 (2x – 1)" Σ V4n + 1 n=0 A) Solve that the provided series is…

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Q: Q3) Evaluate triple integral f " dz dx dy. ェーy

A: Given Triple integral is ∫02∫0y∫x-yx+ydzdxdy

Q: Factorise x6 + 1 as a product of three quadratic polynomials with real coefficients.

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Q: S(t) S(t) = t2 + 3tª. f(t) = t2 + 3t + t3/2. f(t) = t e-3t + e!.

A: The solution is given as

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: What are the future value and the interest earned if $4000 is invested for 7 years at 8% compounded…

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Q: Show that if x is an integer, then gcd(x + 1, x2 – x + 1) divides 3. -

A: First, we find gcdx+1, x2-x+1 Now, factors of x+1 are x+1, 1 x2-x+1 is a quadratic equation of the…

Q: 4. Apply to the initial value problem y' = -ry + 1, y(0) = 0 three steps of the Picard-Lindelöf…

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Q: • Determine and draw the graph of the following equation in R3 : x2 + 212 + 2 8x + 12y – 2z + 35 = 0…

A: This is a problem of multi variable calculus, 3D geometry.

Q: Write the integral that would be used to find the area bounded by y =x² + 1, y = x – 2, x = -2 and x…

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Q: Find the sum of the following convergent series. 3n+1 1 6n-1 n=0 'n + 1 n=16

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Q: cos?. z=1 s divergent or convergent?

A: Given series is ∑z=1∞cos2πz

Q: . x(п) %3D (2)" и() + 3(-) и(п) — 4"u(-п - 1) |

A: Given step by step explanation

Q: Solve for the general and particular solution using Laplace Transform y" +y = sqrt (2) (cos sqrt…

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Q: . Let f(x) = 1— Зх 1 Find a power series representation for f(x) for all x E а. 3'3 1 1 b. By first…

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Q: 5. Consider the power series (25 – 1)" a Show that the series is conditionally convergent when z =0.…

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Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

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Q: F. Directions: Give the converse, inverse, and contrapositive of the following propositions. 26. If…

A: To find converse, inverse, and contrapositive of given statements

Q: Σ (2х — 1)" n V4n + 1 n=0

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Q: Let (V, (,)) be an inner product space and let f,g be vectors in V. If || F|| = 4. ||g|| = 5 and ||…

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Q: too (4 – x)" /n + 5 9n · 7" Consider the power series n=1 Use Limit Comparison Test to show that the…

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Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

A: Test for converges of the definite Integral

Q: Use polar coordinates to evaluate sin (a² + y²)* dA, R where R is the region enclosed by the curves…

A: Here if we put limits in order dr dθ, then the given integral can not b evaluated so we need to put…