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- Find the derivative of the function f by using the rules of differentiation. 7 f(x) = -X417 4 f'(x) =am. 124.Find at least the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. y'' +(x+6)y'+y=0 y(x) = ☐ + ... (Type an expression in terms of a and a₁ that includes all terms up to order 3.)
- NoneLet f be the function defined as, Ր f(x) = [* sin (t³) dt. Determine an expression for f(x) as a power series.Please show all work ง 5. Evaluate the vector surface integral JJ (+2², x + 2y + 32², 5x − 2y + 2³) . Ndo. S Here, S is the sphere Sy²+2 1. = Since S is a closed surface, the outside of S is considered as the positive side on S. Hint: use the divergence theorem.
- A system is described by the action S[r, r'] = [ dt (x² + 4rª + mr³4), r(t) where m is a constant. Find the Euler-Lagrange equation for r = which extremises S. Interpret each of the terms that appear in the Euler- Lagrange equations in terms of Newton's second law. Find a conserved quantity for this system.Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.) (x4 − 9x2 + 2) dx3. Find the margin of error for the given values of c, s, and n. c=0.99, s=5, n=22 The margin of error is
- Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.) √(16 8x + 21x6) dxShow that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use S1, S2, and S3, respectively, for the vectors in the set.) (0, 0) = S={(5, 2), (-1, 1), (4, 0)) Express the vector s₁ in the set as a linear combination of the vectors $2 and $3. 51= Need Help? Read It Watch It Submit AnswerA particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i+ 3xyj + 3y2k. Use Stokes' Theorem to find the work done.
