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8. Evaluate each of the following. (a) L {te-t *et} (b) £{/ sin t cos(t –...
Evaluate the integral (-8 sin(t)- 4 cos() dt ntegral
Evaluate the integral (-8 sin(t)- 4 cos() dt ntegral
The length of the curve { et cos(t) for 0 <t<l is: y = et sin(t)
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
7. Let V be the space generated by the basis B = {sin(t), cos(t), et}. i.e. V = span(B). Consider the linear transformation T:V + V defined by T(f(t)) = f"(t) – 2f'(t) – f(t). Find the standard matrix of the transformation. (Hint: Associate sin(t) with the vector (0), and so forth.) 8. Show that B = {t2 – 2, 3t2 +t, t+t+8} is a basis for P2, and find the change of coordinates matrix P which goes from B...
O 3 Gitt parametriseringa ppgave 7(t) = (cos(t),sin(t), t"), te[0, π], t) - (cos(t), sin(t), t-), og funksjonen f(x, y, z) = (x2 + y2 + 4 . rekn ut kurveintegralet J, / ds
O 3 Gitt parametriseringa ppgave 7(t) = (cos(t),sin(t), t"), te[0, π], t) - (cos(t), sin(t), t-), og funksjonen f(x, y, z) = (x2 + y2 + 4 . rekn ut kurveintegralet J, / ds
e-27 2. Calculate L et sint+e-2t cos st sint+e-2 cos 3t+t%e3+ + ✓at ec [e*sin U2n(t) sin 2t sin 21
please simplify
Problem 2.3 Evaluate or simplify the following integrals or expression as much as possible (show your work). (a) L, 8(t)x(t – 1)dt (e) , 8(at)dt (i) cos(10zt) [8(t) + 8(t + 5)] sin (b) 8(t – T)x(t)dt (f) 8(2t – 5) sin nt dt (c) L 8(t)x(r – t)dt cos (x - 5)|6(x – 3)dx (sin ke (B) e*-2 8(w) (k) 6(r – t)x(t)dt (d) (h) Jt-11 t+9 8(1 – 3)đr Problem 2.3 Evaluate or simplify the following...
6. Use l'Hopital's rule to evaluate the following limits 1+cos (Te sin(z) (a) lim z-+0 log (-1) (b) lim 92I-2 cos(TI) (c) lim r sin Page 2 of 2 0 words
Question 5. (8 points) Find the following: (a) L{t- sin(2t)} (b) C{2* * cos(t)} (c) c- )4+{2+2 +5} 4s S2 + 2s + 5 (d) C-1 6e-3 $2 +1
7- Evaluate each of the following line integrals: (a) /xdy-ydx, c(t)-(cost,sint), 0<t<2π (b) xdx+ydy, c(t)-(cos(), sin,OSIS2 (c) yzdx +xzdy +xydz, where c consists of straight-line segments joining (1,0,0) to (0,1,0) to(0,0,1)
7- Evaluate each of the following line integrals: (a) /xdy-ydx, c(t)-(cost,sint), 0