1. Find the Fourier integral formula for each of the following functions: f(x) = { x +1₁ |x | < π₁ 0, |xc|> π.

Q: One expression for the bearing uses a single angle measure. The bearing using this method is (Type…

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Q: Give a specific application of calculus in biomathematics

A: To Explained : Specific application of calculus in biomathematics.

Q: Use the Linearization Theorem to classify the equilibrium point y = 0

A: To Linearization  dydt=ycos(4πey) and classify the equilibrium point y = 0.

Q: Solve ty' - y = t²e-t assuming t > 0.

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Q: Graph the following function using transformation techniques: f( x)=-3(x+2)^ Description, order of…

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Q: QUESTION 3 Use polar coordinates to evaluate the double integral [[2ydA. R is the region in the…

A: To Evaluate: ∫∫R2y dA where R is the region bounded above by x2-2x+y2=0and below by the line y=x.

Q: Show that the straight lines whose direction cosines are given by the equations al + bm + cn = 0 and…

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Q: 44 If x = a[cost +-log tan² t dy T and y = a sint, then find at t= - dx 4

A: x=acost+12logtan2ty=asintt=π4

Q: Question 29 Solve the system of equations. x1 + 3x2 + 2x3 = 11 4x2 + 9x3 = -12 x3 = -4 O (1, -4, 6)…

A: The given problem is to find the solution for the given system of linear equations.

Q: Question 15 Find the work done by F over the curve in the direction of increasing t. F = Zi + -j +…

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Q: Problem II Consider a linear transformation L₁ : Rª → R³ given below and a linear operator L₂: R³ →…

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Q: Use the divergence theorem to evaluate the surface integral ∫∫S◯F⋅NdS where…

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Q: (3) Determine wether the following a function or not and for functions check if if the function is…

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Q: 19) If f/u) = sinul; then (fog)(3) = ? A) O B) 1 M= g(x)=x²-9₂ c) 6 D) 9 E) None

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Q: Consider the following matrices: 0 0 d11 d21 0 0 d12 d22 0 0 0 0 0 с 0 0 --- D 0 €11 €12 €13 0 €21…

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Q: Find the solution of the following equations using the Jacobi and Gauss Seidel iteration method…

A: Question (b) using gauss seidel method asked and answered.

Q: Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as…

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Q: 4. Σ=11n (443) k 5. Σ.-1 32k+(-1)*4k+1 10k

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Q: Find the Fourier series on the interval (-, π) of teh function 0, −π < x < 0, 0 < x < π. f(x) = {…

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Q: Converting a BASE FIVE decimal into BASE TEN. Step by Step. Complete the table below so that the…

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Q: Consider the following matrices: d₁1 d21 0 0 0 0 d12 d22 0 0 0 0 0 0 с 0 0 0 0 0 0 0 0 €11 €12 €13 0…

A: We can check whether the statement is true or not.

Q: The curves ri(t) = (4t-t²,3t, ²-4) and r₂(t) = (4-t,t³ +8,5t) intersect at the point (3,9,5). If u…

A: Tangent vectors and vector perpendicular to them

Q: Find the greatest value of x2y³ where x and y lie in the first quadrant on the line 3x + 4y = 5.

A: We have to solve given Questions.

Q: A glass sphere given by the equation (x-1)²+(y-2)²+(-3)² = 36 is floating above the plane 2x + y -…

A: The given problem is to find the point on given sphere is farthest from the given plane. Given…

Q: Question 3 ( Consider the differential equation x²y" - 3xy' + 3y = 2x³ – 3x². x³ are = (a) Verify…

A: x2y''-3xy'+3y=2x3-3x2

Q: 28 If √1− xº + √1− yº = a³(x³ - y³) lf dy 1-y6 2 x²

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Q: 4.2 Riemann Sums 103. Use a left Riemann sum with n 4 subintervals to approximate the area under the…

A: Note: "As you can't able to read previous answer so i answered here in handwritten."

Q: Solve the initial value problem of (y" + 4y = 6₂ (t)et ly(0) = 0, y'(0) = 0

A: Solve the differential equations using Laplace transformation

Q: What is about mathematics have change your thoughts that might about it?

A: We have to answer given Questions.

Q: Determine the flux of the vector field F(x, y, z) = (x, y, z) across the portion of the paraboloid z…

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Q: Find the work done by F over the curve in the direction of increasing t. F = -9yi + 9xj + 6zºk; C:…

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Q: Question 4 Evaluate. The differential is exact. (2,2,2) (1, 1, 1) 5 8 1 000 228 ¥3,3 - 3z8 dy+ x²4…

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Q: et r be a three-dimensional real vector-valued function such that r′′ exists. Show that d/dt [r(t)…

A: Given: r is a real vector-valued function in three dimensions, and r'' exists. Our aim is to show…

Q: Question 8 Given the differential equation: A y=c,(1+x arctan(x)) +c Ⓡ (1+x2) y + 2xy - 2y=0 The…

A: Recurrence relation of differential equation using power series

Q: (s+2) s(s-3) b) L{tª(3−2e-³t)²} = a) £¯¹ { L c) L-1 = s+5 (S-1)²+9 ? ||

A: First we will do partial fraction decomposition whenever required then use the formula to find…

Q: Question 14 Using Green's Theorem, compute the counterclockwise circulation of F around the closed…

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Q: Find the area of the given region. Use a graphing utility to verify your result. 2 sin x 1 + cos x…

A: From the picture lower limit of x is π/4 and upper limit of x is 3π/4.

Q: 5. A college dean has received the following results from a department chair about MTH 123, which is…

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

Q: A plane is flying at an altitude of 10,000 meters and is approaching a radar station at a constant…

A: A plane is flying at an altitude of 10,000 meters and is approaching a radar station at a constant…

Q: Evaluate. The differential is exact. (4,4,5) (1, 1, 1) .. O In 80 O In 13 0 80 In ܫܘܐܐܘܠܐܘܐ X dx + 1…

A: In the given problem we have to find the value of the integration . Where the differential is exact.…

Q: Question 19 Evaluate the work done between point 1 and point 2 for the conservative field F. Here…

A: Note: A conservative force is a force done in moving a particle from one point to another, such that…

Q: .1) following transformations: a) x − ¹ {\ c). (s+2) s(s-3) = b) L{^(3-2e-3t)²}= s+5 (S-1)²+9 ? -…

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Q: For the game and mixed strategies, find the expected value. 4 5 (1) 5 2 G=(², 1), - ( + ) r = -3 Let…

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Q: 2. Find the rate of interest i such that a 20-year annuity with payments at the end of each year has…

A: The rate of interest is assumed to be i. The accumulated value for a 20-year annuity with payments…

Q: Find the characteristic equation of the given matrix. [8-15 2] 031-1 0 0-6-6 0 0 0-5] A =…

A: The given matrix is A=8-1    5   20   3   1-10   0-6-60   0   0-5 We have to find the characteristic…

Q: 1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) =  x2 + e9y ln(x-y). ○ Compute…

A: The given problem is to find the gradient vector of the given surface at point and to find the…

Q: Let A = {9k +7 ke Z} and B = {3j+1 je Z}. Show that AC B. :

A: Let, x ∈ A    =&gt; x = 9k + 7 for some k ∈ Z.

Q: DETAILS TDOORS. (a) If f(x) MY NOTES find the Taylor polynomial centered at a=0. Write at least 4…

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Q: 2k+1 2. ΣK=12k²(K+1)² 3. Σ=1 tan-1(k + 1) – tan^1(k)

A: Using limit comparison test:

Q: (a) 64.

A: The objective is to evaluate 64. The rising exponent xm is given by  xm=xx+1x+2⋯x+m-1, where x∈ℕ and…