1.1 Show that if |z| < 1. then lim z" = 0. %3D 1.2 Show that lim Vn = 1.

Q: Q.3 An experiment gave the following values : v(ft/min) 350 t(min) It is known that v and t are…

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Q: Г2 0Т Г26 For A = |1 3 and b a least-squares solution of Ax = b is 1 51 . What is the least-squares…

A: A = 201331,  b = 2600,  x^ = 5-3 Least square error (e^) = ||b-Ax^||  Now, first find the value of…

Q: Solve for the laplace transform x(t) = 4(t/5) e-t/6

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Q: Question 15 You are given the data points (i, Yi) for i = 1, 2, 3: (2, 3), (1, –8), (2,9). If y = a…

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Q: -25 Find the characteristic equation of the matrix 3 5 C. 22 -32-25 = 0| A. 22-32+5=0 B. 22 +72+5=D0…

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Q: Consider the quadratic form f(x1, x2, x3) = x+ x+4.x+ 14x1x2. 1 is (i) The maximum value of f(x)…

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Q: Given d, = and dy = Then d, and d, are not - conjugateif Non of these O D

A: Given d0 = -11  and  d1 = 56

Q: For all x E R, e* = n=0 n! Express f (x) = x²e* as a power series. Find the third-degree Maclaurin…

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Q: Question 34. Let A be a symmetric matrix. Suppose that u and v are two eigenvectors of A…

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Q: +oo 22n (2x 1)". Vn2 +1 Consider the power series n=1 1. Use alternating series test to show that…

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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: Apply the Laplace transform to the differential equation, and solve for Y(s). y" + 4y = 2(t –…

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Q: In(z2) dz Is the improper integral convergent or divergent? Solve for its value.

A: So, we will solve this integral using by-parts formula Integral I = ∫-10ln(z2) dz We can write this…

Q: Consider the following. W = cos(x - y), x = t², y= 51 (a) Find dw/dt by using the appropriate Chain…

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

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Q: Consider the linear transformation T : M22 P2 given by a T(" D= = (a + 26 + c+ d) + (a + 26 + c+ d)æ…

A: Let us considre the linear transformation T:V→W Kernel of T is obtained as Ker(T)=v∈V|T(V)=0 Range…

Q: Given the series, is it convergent or divergent? Eto 4+cos?n n%=1 3n-Vn n%=D1

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

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Q: 2. — 4х, + 2х, — — 6 4x1 2x2 Зх, — 5х, 1

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Q: –10° | The eigenvalues of 1 are 3 and

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Q: Question 10 Consider the linear transformation T : P2 → M22 given by [4a + c T(a + bx + ca2) : You…

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Q: Let Y C R² be the set {(x, y)|0 < x < 1,0 < y < 1 and y E Q if x # 0} endowed with the dictionary…

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Q: If lim f (x) = 2 and lim g(x)=-1, then lim 3/(х) - 2g(х) is ... f(x)+ g(x) Jika lim f(x) =2 dan lim…

A: Limit of the rational function

Q: Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) =…

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

A: The solution is given below. Hope this helps.

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R?, where 31 b1 b2 C2 7 3 10 22 b] what is the…

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Q: The task is to determine and sketch the domain of the function In (b – a² + 4) V36 – 4a² – 9b² g(a,…

A: Here function is given in terms of a and b ,We will sketch the domain by plotting a along horizontal…

Q: Evaluate: f (3x2 - 20x)² dx

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Q: Let A = ⟨1, 0, 2⟩ and B = ⟨6, −2, 3⟩. Solve for projAB. Then, find the angle between projAB and B

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Q: A doll-manufacturing company wishes to create a display box with a square base and open front side.…

A: Given Let the side of square base of open box is a and height is h. also given surface area is 486…

Q: Find the solution of the following IVP using the characteristic method : u + uu= y у , и(1,у) %3D Зу

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Q: Let W he the subspace of M(R) defined as follows w - Span ( 1-L: D a. What does a typical vector in…

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Q: -3 Let A be a 2 × 2 symmetric matrix satisfying A -3 and A 3 17 with the spectral decomposition 3 a…

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Q: Evaluate the Inverse Laplace Transform F(S)=T51)² -2

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Q: dx 3. Evaluate the integral 1 = Jo?+6x+10 Include 4 decimal places on your computation. a. single…

A: According to bartleby rule we can solve only first question or 3 subparts of first question

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

A: Given : The given series is ;  ∑n=1∞un = ∑n=1∞sin2tan-1n - π2tan-1n - π To find : To check whether…

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: 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: Suppose that T is a linear transformation such that T T Write T as a matrix transformation. For any…

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Q: Question 18 Let B = {1+x, 1 – x2, x + 2x} and p(a) = 7+ 10x + 11a?. You are given that B is a basis…

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Q: Q3/ Find the IVP for the differential equation X y' - 3xy'+ 68y=o, that satisfies the initial…

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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: ocar bookstore earned a total of Php7.510.00 for the day. If the expenses incurred for today reached…

A: To find the solution of the above given questions :-

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

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Q: Let T : R² → R² be defined by 7(E)-E 2. X2 a If B = is a basis for R“ such that T'|B is a diagonal…

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Q: Question 30 Consider the linear transformation T: M22 → P2 given by a T = (a +6 +c+ 5d) + (a + b +…

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Q: 1. The area B is given by { x² (x, y, z) E R² y? < 1, 2 = x² – y? B = 9 Assign Stokes' integral…

A: Given : area B is given by      B=x, y, z∈ℝ3 | x24+y29≤1, z=x2-y2 Assign Stokes' integral theorem…

Q: Theoremiif fi Ia b}-sR is cantinhons function then fERiemann [arb}. Does the Converse af the…

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

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

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