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16 Use substitution to find each of the following (a) (sin rcos.rdt (0) (tan'r. see'r de...
Use substitution to find the Taylor series at x = 0 of the function 16 sin(-x). What is the general expression for the nth term in the Taylor series at x = 0 for 16 sin (-x)? 00 (Type an exact answer.) no
Integration by substitution 1. Find each of the following indefinite integrals using integration by substitution: dz (a) / (xºcos(x4) ) do (c) / (sin(2) cromka) die (e) / (24) do (a) / (2.eller) die (0) / (zlog.cz) Integration by parts 2. Find each of the following indefinite integrals using integration by parts: (a) / (+cos(x)) dx (c) / (vVy + 1) dy (e) / (sin”(w) ) at (8) / (sin(o) cos(0) ) da (b) / (x2=+) di (a) / (x2108_(2))...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...
3. Use the trigonometric substitution r = a sin(0) to evaluate the following indefinite integral: da
use residue theorem to evaluate the following integrals 16) cosa 30 de 5- 4 cos 20 17) COSI det (x + 1)? sin 3x dx 18) sin x dx (x² + 4x+5 19)
Evaluate each of the integral by performing the given substitution. (Use C as the integration constant. For the function of "sen()", use "sin()". For example, "sen(x)" is written as "sin(x)". sen5(e) cos(®) de, u = senco)
Problem 13. You don't have to use the Weierstrass substitution for trigonometric integrals. Sometimes you can find a substitution that works more easily (fewer steps) than the Weierstrass. By "trigonometric integral", I mean the integral of a rational function of sine and cosine. You can use the Weierstrass substitution with integrals like SVsin(@) de, but you won't get an integrand having an "elementary" antiderivative. However, the Weierstrass substitution always yields an integral we can evaluate explicitly, whereas an ad-hoc flavor-of-the-day...
3. Show that the differential equation 1 d de sin sin 0 de de sin20 Lastl leads to the associated Legendre equation if we consider the c= cos0, A- v(v+1), ux)-e(0)
e-30 sin() -1 backward substitution method 4. Given A = sin(t) cos(t) tanto find the following 0 a. Matrix of minors (2pts) b. Matrix of cofactors (2pts) c. Adjoint matrix (2pts) d. Determinant of A (2pts) Inverse of A using the Adjoint matrix. (2pts) e. 1 v T.
Use the given information to find the exact value of each of the following a sin 20 b. cos 20 ctan 20 sin 0 3 4 0 kos in quadrant 11 a sin 2-0 (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression Rationalize all denominators) b. cos 20 = (Simplify your answer. Type an exactamwer, using radical as needed. Use integers or fractions for any numbers in...