(27) Consider the piecewise function f : [-L, L] –→ R given by Ja + L, if – L

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A: Problem 1 :- x + xy =C;   C is arbitrary constant. x + xy =C…

Q: fex Sin X %3D

A: According to guidelines we solve one question (2).

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A: Given the area enclosed by the loop of the curve y2 = x(x-3)2 is revolved about the x-axis. We have…

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Q: 25: Using a suitable Fourier- Series expansion for 0 S x ST: A) Show that: x(n -x) (cos 2x cos 4x .…

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Q: 1. The transport PDE, du has a family of solutions u = f(z – vt) where f can be any function. (a)…

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

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Q: A culture of bacteria in a laboratory is subjected to a substance to decrease the number of bacteria…

A: Set e-t2+5t+3 equal to 100 and then solve for -t2+5t+3. e-t2+5t+3=100ln e-t2+5t+3=ln 100…

Q: (푸+이)- (+0) + . 13. Answer the questions by comparing the equation, f(x) = 7 cos (x+ 9 +1, to the…

A: Solution

Q: 1 (a). 22 + 3 (b). (c). z2 – 2' 2 – 22

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Q: The eigenvalues of x2y*-xy'- ay = 0, v(1)= 0, v(e) = 0 ks Hint:[Use only case 3]

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Q: 20 8. Compute the crossing number for each of the following graphs.

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Q: Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y) at the point (1,…

A: Let us considre a two variable function z=f(x,y)  Then the equation of tangent plane  at (a,b) is…

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Q: R Solve the following 2 order ODE using me method of variation of parameters. y"-4y' + 4 y (12 x2 -…

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Q: 4. Find a vector that points in the opposite direction as ā = (-3,–14,2) with a magnitude of 32. 5.…

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Q: Problem 22.8 Solve by Laplace transform Utt - 9urr = 0, 0 0 u(0, t) = u(T, t) = 0, %3D u (x,0) = 0,…

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Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec (2xy),…

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Q: Consider the real sequence {a„} given by an = In(n + 1) – In(n + 2), ne Z20 = Nu {0} Justify whether…

A: Introduction: The sum of an unlimited number of numbers connected in a specific fashion and listed…

Q: Problem 3. Recall that a" = for all a > 0 and all b. lim (1+ -)" (1) Compute the limit lim (1+ -)"…

A: 1)  We need to find , limn→∞ 1 + 1nn First we will breakdown 1 + 1nn using binomial theorem ,  1 +…

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Q: What is the approximate volume of the cone below? 7 cm 10 cm A 70 cm B 183 cm 3 с 549 cm D 733 cm 3.

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Q: A. Solve the following 1" order, non-homogeneous linear ODE: dy cos? x sin x +y (cos x) = 1 dx

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Q: Describe the graph of the equation. r = (6 – 21) i+ 10rj O It is a line in 2-space through the point…

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Q: (a) Find all cosets of the subgroup 4Z of Z. (b) Find all cosets of the subgroup (4) of Z,2. (c)…

A: Since you have posted a question with multiple sub-parts , we will solve first three subparts for…

Q: The eigenvalues of x²y*- xy'- ày = 0, y(1) = 0, y(e) = 0 is Hint:[Use only case 3)

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Q: Consider the equation (34)x = (3y)s where x and y are unknown. The number of possible solutions is

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Q: if a 20 f(x) = if a <0

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Q: the row space and for the column space of that matrix. [1 3 0. 0 0 LO 0 0 1 1 1 6. 4. A = 1 -3 Enter…

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Q: Exhibit a commutative ring R and an element x E R such that Z CR and x is NOT prime but irreducible…

A: Take R = Z[i√5]  Clearly, R is commutative ring and Z ⊆ R  Also, 2,3 ∈ R are not prime but…

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Q: a. The zero vector 0 is in ker(A) b. If x and y are in ker(A), then so is z = x + y. c. If x is in…

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Q: (1) Show that the series n+1 n-1 and n3 +1 n3 – 1 n=2 converge. Be very clear about the steps you…

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