Problem 1 Use residues to verify the formula poo cos(3x) – cos(x) dx = a Jo...
dx 0 x show all work! 4. [12 pts.] Use residues to evaluate the integral Jo +1
cos'x dx sin 3x dx 2. an 45 sin cos'xdx 4 sin'xcos'x dr 44 sin'x cos'r dr 6. sin'xcosx dx 8. Jo sin'x cosx dx fa-sin 2x)' dx sin x + cos x dx 10. 9 f sin'z dx cos'x sin'x d 12. 11 sin'x Vcosx dx 14. 13. cot'r sin'x dx 16. cos'x tan'xdx 15 dx sin x dx 18. 17 1-sin x cos x tan'x dx 20. tanx dx 19 sec'x d sec'x dx 22. 21 tan'x secxdx...
For cos x cos 3x – sin x sin 3x = 0, use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval x (0,7). The answer is 21 22 = 23 = and 14 with xi < 22 <<3 < 24.
Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0) Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
1. Using the half-angle formulas fine the EXACT value of cos(22.5o) 2. verify the identity cos(3x)=(1-4sin2(x))cos(x) 3. find the EXACT solutions in the interval [0,2pi) sin(2beta)-2cos(beta)=0 ******Please do not use and decimals in the set or answer process***** Thank you so much
4.4 EXERCISES 1-4 Verify by differentiation that the formula is correct. V1 + x² 1. + c 1 x²/1 + x2 dx X 2. [ cos²x dx = įx +sin 2x + C 3. tan’x dx = tan x - x + C 4. [ xva + bx dx = 2 (3bx – 2a)(a + bx)3/2 + C 1562
1 x + x² - 12+)-(-X ² + 3x) dx + J (-X +3x)-(- Use the DISK or WASHER method to set up #3 - 6. 3. Find the volume of the solid formed by revolving the region bounded by y =x', y =1, y = 0, and x = 2 about the line x =2.
Use the substitution formula to evaluate the integral. 1/2 COS X s dx (5+5 sin x) 0 3 OA 1000 OB 3 200 OC. 3 200 OD. 12 125
Problem 1. Consider the harmonic function 2 cos 3x 1xs5 Investigate the validity of the numerical differentiation process by considering two different values for the number of points in the domain: (a) 11, and (b) 101 Plot the exact derivative of function y vs approximate (ie numerically determined) derivative of function y for both cases Qi. What is exact value of " for x=1.6? dx dy for x Q2. What is approximate value of 1.6 when number of points is...