(e) u + tu = 1,u(x, 0) = f(x) Solve the t X following PDEs using the method of characteristics (e) u₁+tu× =1, u(x, 0) = f(x)
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- Find p′(t), p′′(t), and p′′′(t) for the function p(t) = t^(100)+ 4e^(t)+ 16. (You can use rules or shortcuts, but you must write which rules you’re using.) Give clear steps and explanations.Q/IF it was AY ₁2) = -12 ℗ Y³ (2) = -12 ⒸY³ (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13 = X+1 X-1 Y = Not of the above so y" (2)A particle has zero velocity initially (i.e., at time t = 0 ) and its acceleration at t seconds is a(t) = 72t - 4t³ meters-per- second per second. During the time interval [5, 8] seconds, (i) the average acceleration of this particle is -689 (ii) the average speed of this particle is | # meters-per-second per second meters-per-second.