3x + 48x = 5 cos(4t) 3x'' +53x = 5 cos(4t)
Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.
A: Given curves are y=x2-3x y=x3+x2-12x Take y=fxHere, fx=x2-3x y=gxHere, gx= x3+x2-12x
Q: 1. Find the inverse Laplace transform y(t)=L−¹[Y(s)] where (b) Y(s)-e-³s (25-3) $²-49
A: We will be using the formulas of inverse Laplace L-1{a·fs+b·gs}=a·L-1{fs}+b·L-1{gs} L-1{1s-a}=eat…
Q: [2] e. The bell from Question 3 is struck by an external ringer as shown in the photo below. The…
A: Here beam is perpendicular to surface so we can use equation of normal line to find equation of beam…
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Q: Find Taylor Series for F(x)=sin(x) at (x=π/4), find Sin(46°)
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Q: Consider the following matrix A 3 1 1 4 1 -1 1 5 ) Show that the matrix A is positive definite. >)…
A: We know that , A matrix is positive definite if all of it's upper left determinants are positive. We…
Q: a) b) Find the area of the triangle determined by the given point P₁(1, 2, 4), P2(1,-1, 3), P3(-1,…
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Q: Find the area of the surface formed by revolving the ellipse about the z-axis (an ellipsoid) y² + a²…
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Q: Question 9 Use the method of reduction of order to find a second solution of the differential…
A: Introduction: When there is higher order ordinary differential equation with variable coefficients…
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Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹ x² + y² O 3 4 y x
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Q: Find the Laplace transform Y(s) of the solution y(t) of the initial value problem where…
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Q: Find the radius of convergence, R, of the series. R= Σ n = 3 I= X²+2 4n! Find the interval, I, of…
A: We use ratio test.
Q: o find the smallest positive root of tan x-x=0 which of the following re-arrangemen propriate? e the…
A: The following steps are used to find the numerical solution of the equation fx=0 by the fixed point…
Q: Find the Taylor or McLaurin series for the following functions f(x) = xe-*, a=0
A: Here f(x)=xe-x,a=0. We find the Maclaurin series of f(x).
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Q: E=2*10^5 I=30000 L=600 W=25 y = dy dx W 120EIL = 120 FIL (-5X² + 6(³X²-1²) ū assume as р 38, P = =…
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Q: convergence. a. Σ Ξ (-1)"x2n b.00 3"
A: Ratio Test for convergence of a series . Series ∑an is convergent if limn→∞an+1an<1
Q: Example 2 Let A = [aij], B = [bj] be two nx n matrices in Mnxn with inner product (A, B) = tr (ATB)…
A: Given A = 1011 , B = 0200
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Q: The function y= 98.6 + 0.3 sin(í/12 x – 11à/12) models variation in body temperature, y, in °F, x…
A: For a function y=Asin(Bx+C)+D A is amplitude 2πB is period C is phase difference D is vertical…
Q: Q 11: Determine the measure of the central angle that is formed by and arc length of 5 cm in a…
A: Solution: Given, Arc length(s) = 5 cm Radius(r) = 2.5 cm Now, We know that arc length(s)…
Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is fals statement,…
A: given statements 5. A cat is a fish. If a cat is a fish then the piranha is a mammal. Hence the…
Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x +y + 2z = 1…
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Q: 72 n²+1 7. Given a series En=1(-1)"-1 a. Determine whether the series absolutely converges or not.…
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Q: Thank you understood theoretically, but unable to visualize. Can you please draw a rough diagram to…
A: As per the question we have to give a diagram helping the proof and to visulaize the phenomenon of…
Q: Find b and c so that y = 8x² + bx + c has vertex (7,5). b C =
A: Here given that y=8x2+bx+c and has the vertex at the point (7,5) since the line of symmetry is the…
Q: By changing the independent variables z and y to u and r by means of the relations u=z-ay, v=z+ay,…
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Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…
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Q: Let X be a normed space. (a) If E₁ is open in X and E₂ C X, then E₁ + E₂ is open in X. Proof: (a)…
A: It is given that X be a normed space, E1 is open in X and E2 be any subset of X. We have to explain…
Q: 3 (i) Given that 3x³ +5x2 + px+8 = (x-2)(ax² + bx + c), find the value of each of the integers a, b,…
A: Here given that 3x3+5x2+px+8=x-2ax2+bx+c We have to find the value of the integers a, b, c, p and…
Q: Find the minimum and maximum values of the function on the given interval by comparing values at the…
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Q: Romberg integration for approximating f f(x) dx gives R₂1 = 2 and R22 = 12 then f(0) = O 14 O 4 O…
A: Here given integration as ∫-11fxdx and given R21=2, R22=12 Now, According to Romberg integration for…
Q: let a₁, a2 and a3 be the columns of A, let B = (a, a, a) and let H = span(B). a. The number of…
A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…
Q: Find the solution to the initial value problem: x2dy = 2y dx y(x) = y(1) = -2
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Q: Suppose, and no are the smallest of two positive integers so that 300x is a perfect square and 300y…
A: The given problem is to find the values of x and y and sum of value of x+y for which smallest…
Q: Describe the right-hand and left-hand behavior of the graph of the polynomial function.…
A: Right and left behavior of any polynomial depends on its degree ( highest power of x ) and co…
Q: a) Volume of the function f(x,y)=√x+y over the triangle region bounded by x+y≤l, x≥0, v 20. b)…
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Q: 10. Find f'(x), f"(x) and f f(x) dx for the following power series a. f(x) = 1 n-³ xn b.Σ=1 (x-1)+1…
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Q: Find Maclaurian series for f(x)=ex and e-0.2
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Q: Prove or disprove the following statements: (a) If (ab)n+1 = an+¹fn+¹ a, b = G, n=1,2,..., then G is…
A: In this question, we have to prove or disprove the following statements : (a) If abn+1 = an+1bn+1…
Q: Let X₁ be a closed subspace and X₂ be a finite dimensional subspace of a normed space X. Prove that…
A: Here we have given that X1 be a closed subspace of a normed space X. So, the quotient space XX1 is…
Q: 41. Find the value of x. to 150° 34°
A: Formula: The external angle is half the difference between measure of intercepted arcs.
Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…
A: 5. False Because given that a cat is a fish Then the condition is if a cat is a fish then the…
Q: Does the series k=1 O converges absolutely O diverges Does the series converges conditionally 1 k6+5…
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Q: Given the function C'(r) = (r − 1)( − 5r + 3)³(r − 2)5, - its roots are and their multiplicities are
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Q: Determine the form of a particular solution yp of Ур y" + 4y = x cosx. Do not solve the equation.
A: Here given the differential equation as y''+4y=xcosx or D2+4y=xcosx where D=ddx
Q: A plane flying at an altitude of 35,000 feet at a speed of 690 miles per hour releases a bomb. Find…
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Q: In exercise 6 to 10 use the rule method to describe the following set. 6.A={3,7,5,9,11,13} 7.…
A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…
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