Let Tulx): be the Taylor Polynomal fcx)= en (i+x)at ano ot degree 6 ot the function. Approximate frr) by Tolx), find all positive valved ot x for which this approx 1S within o-00 ot the right answer. luse the alternating seried approx.)

Q: Use the parallelogram method to find the following sum v + w when v = (-5, 4) and w= =(5, 4). (0,0)…

A: We have to find the following sum v + w, when v = (-5,4) and w = (5,4) by using the parallelogram…

Q: Let (a, b) belong to Zm ⨁ Zn. Prove that |(a, b)| divides lcm(m, n).

A: Given: a, b∈Zm⊕ZnWe need to prove that a, b divides lcmm, n.

Q: What is the cocfficient of x" in the power series expansion of v1 – 5x?

A: Given,

Q: Aforce F: 2i+j-3K is applied to a space craft with Velocig V. 3L-J- Express FasThe Sum of aretor…

A: F = 2 i + j - 3k,v = 3 i -j

Q: nxn For any A, B in R prove that Įrank(A) - rank(B)| ≤ rank(A + B) ≤ rank (A) + rank(B). }

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Q: Q=- Find the Zero and its oider for the function fiz) = 1- Ki+Z+ ¢ ?

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Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: Let foo = x-x -1,06 <2 Use the Fixed-Point iteration method to approx imate the roo- of FOu accurate…

A: We have to use fixed point method to solve given equation.

Q: Q3)b) Use Taylor theorem to show that 2x-2를 <2 sinz <2z-2% +2를1

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Q: Prove that: Using Cauchy's Residue Theorem dz = 1+z² 8

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Q: =1 using Cauchy's Residue theorem.

A: Cauchy's Residue theorem: Let fz be analytic within and on a positively oriented simple closed…

Q: Find x and y for which the following equation is satisfied: x+2 = - 5+i i-5

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Q: - Z Let h(x, y, z) Then 3 (x² + y2 + z²) 2 ah А. (x, y, z) В. (x, y, z) = ', Y, dydz C. As a…

A: Here is the solution

Q: Let f(x) = e* cosx. a) Find the 2nd order Taylor polynomial P₂(x) for f about xo=0.

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Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: Evaluate the integral JS2dx. (a) Se2+ C (b) 2 +C (c) (1/5)e$+2 + C (d) 3eS+3 +C (e) (1/3)e**3 + C…

A: We use substitution method

Q: i) what ins the nE Taylor polynomial , la) of a fune bien fx) at x-c? What does Taylor's Theorem say…

A: We have to find the Taylor's polynomial pn(x) of a function at x=c

Q: 6. If F = Pi + Qj + Rk, prove that div (curl F) = 0

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Q: xe x145)dx (√3x + 1 + xe d) Į sec² x tan² x dx

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Q: find the Taylor Series for Jow= lax about

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Q: Q6. Use Taylor's Theorem to prove that if x > 0 then, 5 1+

A: Given,x&gt;0 To prove: 1+x12-1+x3+x29≤58!x3

Q: fo )= In [) 10+3 OC-1 i) find the doman of defnition of t) Show that fö injectve that Fs Mechve iit)…

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Q: et A be 4X4r nas non-brivial . -son-

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Q: 5. Prove that if x, y ER, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: We now prove that if x,y ∈ ℝ , then x+ y≤ x+y with the help of given three cases.

Q: A. В 1 x a n

A: From ven diagram we can get answer easily

Q: 1. Divide the interval [a,b] into n = 4 subintervals of equal length and compute A) the sum of the…

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Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: # Find the rate of of f at plose,-1) and find the direetion of of the given funetion. gre atest…

A: Greatest increase of function f is magnitude of gradient of function f. Greatest increase of…

Q: Q4. Let A E Rnxm, n ≥ m. a) Use the SVD of A to deduce the SVD of ATA. b) If m = n and A is…

A: Given: The given expression is, A∈ℝn×m , n≥m a) To use the SVD of A to deduce the SVD of ATA b) To…

Q: d tant lea) de tan' L) Itx? 2x THlege THe" ux 2) la 2x ln x Ids 2 lox t 2 y de 4(2/ax+2) 3) fL7)-6…

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Q: Use Green's thearem to evalute where c is the Loundarde of the regian cncdlosed by and for ラメラ0

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Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: # if Alu) is a differentimble veetoru u and l A(W) Il = 1 . fonetion of Prove that dA is…

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Q: b) У + 8 1 4x on [1,2]

A: The given curve is:y=x48+14x2        on  1, 2

Q: First prove Schwartz inequality; |x ・ y| ≤ ∥x∥∥y∥ Then show ∥x + y∥ ≤ ∥x∥ + ∥y∥ Then show d_2 (x,y)…

A: 1) Let's assume that u is non-zero, then &lt;u, u&gt; is also non-zero and let's define a = &lt;u,…

Q: f (て) be a top. space 3.ト X-Tab, cidiel (xて) be top space %3D %3D et A= {bj. FindO A Tb,d] %3D 2.…

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