3. If $1000 is invested at 10% compounded continuously, the future value S at any time t (in years) is given by S = 1000e 0.1t a. What is the amount after 1 year? b. How long before the investment doubles? [3]

Q: (g) F= R, V = {ve R²: sin(v₁ + ₂) = 0}; (h) * F=R, V = {v € R²: e¹¹ = 2e¹2}; (i) F= R, V = {v € R³:…

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Q: Problem 3. Let VCR³ be the region bounded by the planes z = 0, z = 1, and the surface defined by z²…

A: Solution :

Q: -2 Evaluate: £²³₁²[(x²-y²)²] du dt

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Q: Σ (j + 2)² = j=11 = first step 2nd step 3rd step 4th step final answer

A: The given summation is                   ∑j=11n(j+2)2 To find the given summation we shall use the…

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Q: (4)Let K be integer ring module 12 and let I=([4]) and J=([6]) be ideals of K. Then [2] belong to…

A: Given that, K=Z12 and ideals I and J are such that I=([4])=4Z12={0,4,8} J=([6])=6Z12={0,6} Now,…

Q: Consider the following Gauss-Jordan reduction: 1 00 01 56 70 0 0 100 56 7 0 →>> 56 7 O 69-69 810 010…

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Q: A linear time-invariant system (A, b, c) is modelled by the state-space equations x(t) = Ax(t) +…

A: Here we need to show that wether system is controllable and observable.

Q: R. Map A A= {(8, 13), (8, 9), (9,8), (9, 11 ), ( 11, 8), ( 11, 9), (13, 8), (13, 14), ( 14, 16), (…

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Q: defined on the set 10 Consider the vector field F(x, y, z) = (= + 2²,5 = +2²) N = {(x, y, z) € R³ :…

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Q: Evaluate: ſ³³ S±₂ S₁°(4x²y — z³) dz dy dx

A: We have to evaluate, ∫03∫-24∫10(4x2y-z3) dzdydx

Q: 4. The shell of a spacecraft (see Figure 2) is a union of two surfaces : • S₁ is part of 2² + 4y² +…

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Q: 9. Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y"…

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Q: 4 Find the area of the region bounded by x = 2y² +1 and the y-axis using the horizontal strip.

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Q: 1. Given that S² dx 1+x² = tan¹ x = = expand the integrand into a series and integrate term by term…

A: We have to expand the integrand into a series and integrate term by term obtaining result which is…

Q: 5. The variables x and y are related by the following differential equation. dy x+y = dr x-y By…

A: Solution :

Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

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Q: Question: Verify Green's theorem in the plane for (x³ − x²y)dx + xy²dy, where C is the - C boundary…

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Q: dV = r dz dr de where R: 0< Draw the solid R. z = √√3x² + 3y² and below the Duom solid

A: Using the volume of cylinder and the solid is given as,

Q: Consider the following two player bi-matrix game 19 6 19 1 -10 21 B = 0 -8 -5 A = 7 12 6 2 14 16/ -9…

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Q: Draw a direction field for the differential equation y' = −y(5 - y). Based on the direction field,…

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Q: Let f: RR be a continuous 27-periodic function whose Fourier series is +∞ 1 1/2 + + /20 cos(nx). n=1…

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Q: 6. Evaluate the line integral ² dr+z²y dy where C' is the rectangle with vertices (0,0), (5,0),…

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Q: 2.a. Find the maximum and minimum values of the function: y = 3x² 18x +31 -

A: We have to find the maximum and minimum values of the given function y=3x2-18x+31 .

Q: Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis, and…

A:

Q: Determine the general solution of the following differential equation: (D²-4D+4)y=(6e2x)/(x4) O A. y…

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Q: equations (b) P Identify the surfaces of the following equations by converting them into in the…

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Q: Evaluate: ²₁¹ (x² - y²) ²1 x+y du du dt

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Q: Find the wronskian of f1= x2-6x, f2=x2+6x, f3= x2-3

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Q: F(s) = s+s Ans. f(t) =1-e

A: “Since you have asked multiple questions, we will solve the first question for you. If you  want any…

Q: Q5. Use Lagrange Multiplier to find the minimum distance between the origin and the line (x=51 +3, y…

A: Solution :

Q: 5. Use the inversion algorithm to find the inverse of the matrix (if the inverse exists). 1 0 1 1 1…

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Q: 1. The sea level rises and falls above mean sea level roughly twice every day due to the daily…

A: Let us start solving the problem step by step  Given data:

Q: 3. What is the angle between A and B if A.B=0 4. Find (u+v) (2u-v) given that uu=4 u v=-5 and v.v=10…

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Q: Evaluate: ²³²₁₁¹[z³(x + y)³] dz dy dx

A: Given, triple integral  J =∫-43∫-12∫01[ z3(x+y)3 ]dz dy dx

Q: (f) V = {x € R: In converges as noo}, W = R, T(x) = limn → In, I EV; (g) V =R%, W = R, T(x) = -1n,…

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Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: Let (an) be a numerical sequence such that lim |an|¹/n = 7-8 ∞ gence of the series 5a," is (A) 83…

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Q: A feedback control system modelled by the differential equation * + ax + kx = 0 is known to be…

A: Problem is solved using concept of Lyapunov Function.

Q: We define a inner product in = U₁V₁ +2U₂V₂ + U3v3 in R³ for u = (U₁, U₂, U3) and v = (V₁, V2, V3)…

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Q: So SAF+1° y¹/3 x7 +1 (Hint: Change the order of integration to dy dx.) Y dx dy.

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Q: Evaluate: 2²₁₁ (4x²yz - ) dz dy dx

A: evaluate  I=∫23∫-14∫104x2yz-z44dz dy dx integrate the function I=∫23∫-142x2yz2-z52010 dy dx…

Q: 1. Use the method of undetermined coefficients to find the solution of the initial value problem y"…

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Q: 2 m Find the angle theta. a = 5. b = 3. im N 1m D

A: Solution:-

Q: (0₁-≤x≤0 Q.7 (a) Obtain the Fourier series of the function f(x) = { 1,0 ≤x≤# (b) Show that, f du =…

A: For second part we use the Fourier cosine integral representation of a function

Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

A: The region is

Q: 6 The flux of the curl of the vector field F(x, y, z) = (y², r, 2) through the surface Σ = {(x, y,…

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Q: Find and classify the critical poruts g a te functions f(x,y) = exsing f(x, y) = excosy

A: 1 Given function is fx,y=exsiny. We have to find the critical point of fx,y. Differentiate…

Q: (E-₂) = given the linear transformation T: R³ → R² where T 7 (EFD)-6) and + (ED-C¹₂) a. If it is…

A: