(iii) Lagrange mean value theorem. (iv) Cauchy mean value theorem.

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Q: 9. Find the particular solution to the given initial value y''' - y' 0; y(0)= 2, y' (0) 3, y'' (0)

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Q: The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data…

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Q: 2. Find a function f and a number a such that f (t) 1+ -dt = tan t2 Give proper reasoning.

A: Topic:- application of integration and derivatives

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Q: Solve the following linear system by Gaussian elimination. x1 + x2 + 2x3 = 9 -X1-2x2 + 3x3 = 6…

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Q: Question 10. Find the Fourier cosine series forf (x) = x 72 if 0 ≤ x ≤ 1/1/0 if / ≤x≤L on 0 ≤ x ≤ L.

A: Given fx=L2        0≤x≤L2                                        0≤x≤Lx-L2    L2≤x≤LTo find:…

Q: 10. A liberal arts college has one thousand students. The numbers studying various languages are:…

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Q: Compute the optimal rank-2 approximation of the symmetric matrix 5.00 0.50 -1.50 0.00 0.50 5.00 0.00…

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Q: Question 2.2: Find all the values of the given expressions: (a) In (1+i); (b) 1'; 1+/ (c) (1 + i)¹**

A: (a)    we know that    x+iy=reiθ          where x=rcosθ  ,  y=rsinθ    and  θ=tan-1yx…

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A: Let A and B be two events with P(A) > 0. Then the conditional probability of B given A, denoted…

Q: Question 1 Determine which of the following functions are a bijection from the set of real numbers…

A: f(x) = x11 - 7x7 is not one-to-one, as           0 ≠ 71/4 but f(0) = f(71/4) = 0   Consequently,…

Q: Calculate the Fourier series of the periodic function depicted in the figure below.

A: This is a question from Fourier Series.

Q: Question c. Thanks

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Q: I. Evaluate S x² +6 x³ + 3x dx.

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Q: 1. Let F = [y, az³,-zy³] and C: the circle a² + y² = 4, z =-3. Evaluate So Fr'ds through direct…

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Q: 5. (a) Prove that if f is uniformly continuous on a bounded subset S of R, then f is bounded on S.…

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Q: Use variation of parameters to solve the given nonhomogeneous system. dx (x(t), y(t)) = 4x – 4y + 9…

A: Given: Non-homogeneous system:            dxdt=4x-4y+9dydt=3x-3y-1To find: The solution, xt,yt using…

Q: 1.) Find a Frobenius type solution around the singular point of x = 0. x²y + (x²+x) y'=y=0

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A: As per guideline expert have to answer first question only dear student please upload

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Q: Find and classify (if possible) the critical points of the plane autonomous system. (Order your…

A: The critical points for the above equation will be found by equating x'=0,y'=0.

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