[31 Consider the orthogonal basis B 10 of R. 51 Let v = -64 15 a If (v]B = |b what is the value of c? C 2 -4 5. 3.

Q: 4. 4x, + x, + x3 = 7 x - 7x, + 2x3 = -2 = 11 3x1 + 4x3

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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: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Surface are of the surface z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the projection of the…

Q: Find the value of a + b + c + d. (Answer must be an integer) The Differential Equation 2y"' + 3y" –…

A: Let us consider a differential equation L(D)(y)=Q(x) Determine the complementary solution by using…

Q: Given: a, = In(n + 1) – In(n) for n E N Σ An n=1 2.

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Q: Determine whether the following series converges or diverges. If the series converges, determine the…

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Q: j5)(8e1° )

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Q: 1 37 a Let A 1 1 Find a QR-factorization of A. If R = then the 1 value of a is , the value of b is…

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Q: Refer to the System of Linear Equations below. 4x1- X2- X3 -D3 -2x1 +6x2 +X3 -9 -X1 +X2 +7xg =-6…

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

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Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: We have to determine whether the given series is convergent or divergent. Here we use Ratio test

Q: Let A - ( ) a. Show that the vectors lz.A, A² are linearly dependent in Maz (R). b. Deduce that A"…

A: Statement (S1) proves that  I2 , A, A2  are linearly dependent.

Q: Let F: R" R" and r e R". (a) Show that if F(r*) = 0r* is a global minimizer of ||F(x)||. (b) Show by…

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Q: (a) y' = e2y (b) y' 1+ y (c) ry' = y(3 – x)

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Q: Let u(x, y) be the solution of the partial differential equation U =u+ yu,, x>0, y> 0, with u(x,1) =…

A: In method of separation of variables we put dependent variables as a multiplication of two functions…

Q: (-1)" Σ (2n)! R ALL XER, COS = x2 cos (2x) Find power series representation for Then by…

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Q: Suppose that A is a 20 x 15 matrix that has 9 pivot columns. Then: (1) dim(ColA) is (ii) dim(ColA)+…

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Q: Let n = pq be the product of two odd primes. Recall that there are no primitive roots modulo n. Show…

A: We use the idea that if primitive root exists then x^2 = 1 mod (m) has only 2 solutions. The…

Q: Exs Let PE-292]IR be function f(x)%={2 XEG -2 Showthat P3 R-integrable ornot?

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

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Q: 22n -(2x – 1)". +00 Consider the power series E n=1 Vn? +1 Determine the radius and interval of…

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Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where b. A = f(t)…

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Q: 1. The velocity of a rocket is given by v(t)= 2000 ln 14x10 14x10 – 2100t -9.8t,0sts30 where v is…

A: Given vt=2000ln14×10414×104-2100t-9.8t , 0≤t≤30 and t=16, ∆t=2 and True value = 29.674

Q: In solving one real root of tan x = 4x, what will be the appropriate iterative formula for the…

A: Given equation is tan(x) = 4x

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…

Q: What interest will be earned if $6500 is invested for 2 years at 11% compounded monthly? (Round your…

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

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Q: Q4) Find plane area inside the polar functionr = 2 and outside the polar function sin -0) +1 in…

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Q: Convert dzdydx Into an integral of spherical coordinates (6coso p²sinodpdøde psinødpdøde Option 1…

A: We can solve this using spherical coordinates x = p sin(phi) cos(θ) y = p sin(phi) sin(θ) z= pcosϕ

Q: what is the daplace Transform of -2s Use the table of daplace Transforms.

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Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

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

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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: 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: Given de - and d, - Then do and d, are not G- conjugate if Gis Non of these -0.25 105. 0.25 -0.5 -0…

A: We want to find the matrix G for which given vector are not G conjugate

Q: А - (BUC) — | (А — В) UC (А — В) U (A — С) | О Оption 4 Оption 1 (А — В)n (A — С) (А — В — С)

A: 1. As by distributive property A - (B ∪ C) = (A - B) ∪ (A - C) Hence Answer: Option 1 (A - B) ∪ (A -…

Q: Σ (2х — 1)" n V4n + 1 n=0

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Q: Example 7 Sketch the curves (a) r 1 (b) @ = 4. %3D in polar coordinates.

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Q: 9. Find all the solutions of 3x² + 2x + 1 8 (mod 63).

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Q: Q3/ Evaluate Sz Vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

A: 3 Given integral is ∫0π2sinxdx. i We have to evaluate the given integral by using trapezoidal rule.…

Q: Q5) Find volume of body bounded by z = x – y from below and z = x + y from Above inside y = x² ,y =…

A: Volume bounded by the region

Q: 2s - 1 s2 - s -- 2' F(s) = s2 – 4 - 4 F(s) : (s2 + 4)2 1 F(s) = s2 + 3s + 2

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Q: See equation below. Find: a + b -c+ d. (Answer must be an integer) The system x' + y = t; 4x + y' =…

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Q: Wu's job pays $17/hour, and requires him to be at work at least 29 hours/week. He is allowed to work…

A: Solution:Budget line:C = 17h for h⩽40(1.5) (17) (h-40) for  40 ⩽h⩽602(17) (h-6) for h⩾60

Q: Use the algorithm for finding A to find the inverses of the matrices shown to the right. Let A be…

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Q: Given: 1 fett= 구 -1 Obtam the Fruries Seriesi Ans feet- Gia (2n+)t a TT 2ntl Find; ab

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Q: What lump sum do parents need to deposit in an account earning 8%, compounded monthly, so that it…

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Q: Find the particular solution of

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Q: Given: an = In(n+ 1) – In(n) for n E N | Determine if the following is convergent or divergent. (b)…

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Q: Q5) Find volume of body bounded by z = x-y from below and z = x + y from Above inside y = x2 y = 2.

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