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Problem 16. Which of the followings is correct evaluation of 2sin (4nt)8(t)dt 1-2 a. 0 b....
Problem 2. Evaluate the following integrals: a) (t+1)8(t-1)dt b) ſ exp(-+)$(t + 2)dt c) Itsin() 062 – 1)dt
Consider the problem minimize 1[r(-)] = 2 / r,(t)2 dt subject to the conditions r(0) - r(T)0 and the constraint 0 r(t)2 dt 1. = Suppose that r : [0, π] R is a C2 function that! solves the above Let y : [0, π] R be any other C2 function such that y(0) Define problem a(s): (r(t) + sy(t))2 dt and a(s) a. Explain why a(0) 1 and i'(0) 0. b. Show that i'(0)= | z'(t) y' (t) dt-X...
Problem 12. (1 point) Consider the function f(0) = %,* cos(t) – 1 dt. +2 Which of the following is the Taylor Series for f(2) centred at x = 0? O (-1)" A. n1 (2n – 1)(2n); 22n-1 (-1)"(2n - 2) B. n1 22n-3 (2n)! (-1) C. n0 -22n-1 +C (2n-1)(2n)! D. (-1) 2n-2 1 (2n +1)!
Solve for 14(b,c) and 18 (b,c) please 16. Find a set of parametrie equations t d) r(t)-(4t,3 cos(t).2sin(t) the line tangent to the graph of r(t) (e.2 cos(t).2sin(t)) at to-0. Use the qu tion to approximate r(0.1). tion function to find the velocity and position vectors at t 2. 17. Find the principal unit normal vector to tih curve at the specified value of the parameter v(0)-0, r(0)-0 (b) a(t)cos(t)i - sin(t)i (a) r(t)-ti+Ij,t 2 (b) rt)-In(t)+(t+1)j.t2 14. Find the...
(1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution of the initial value problem dy dt with f(0) 0 Find f(t). C. Find a constant c so that solves the differential equation in part B and k(1) 13. cE (1 point) A. Let g(t) be the solution of the initial value problem dy dt with g(1)1 Find g(t) B. Let f(t) be the solution...
(a) Sketch 1 [u(t-1)-u(t-2)] (b) Using the generalized function definition of impulse: "(t)8(1)dt = poſs(t)dt = 90), function $(t) is known to be continuous at t=0. Show that 8(at) (2001).
Convert the followings:- (1) (890.56)16= (…………......)BCD (2) (10111)2 + (205)16 = (…………….)8 .
please answer all questions For 1 2 0, a particle moves along the r-axis. The velocity of the particle at time t is given by r(t)-1 + 2sin(2) Theparticle is atposition x = 2 attimet=4. (a) At time t-4, is the particle speeding up or slowing down? (b) Find all times t in the interval o<t<3 when the particle changes direction. Justify your answer. (c) Find the position of the particle at time t 0. (d) Find the total distance...
please complete all parts Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think Fourier series.) (cos(nt) - 2sin(5rt)e-Jr dt XCj) (b) (5 points) Find the Fourier transform io of the following signal: 2(t) = sin(4t)sin(30) (c) (5 points) Solve the integral: sin(2t) 4t dt (d) (5 points) Use Parseval's theorem and your Fourier transform table to compute this integral: Problem F.7: These are independent problems (a) (5 points) Solve the following integral. (Hint: Think...
3) Consider a particle moving in the circular trajectory x(t) = 2 cos(t) and y(t) 2sin(t) subject to the potential U(x, y)-x2 (2 - ry) (a) (2 marks) Use the chain rule to calculate d at t = 0. (b) (3 marks) Calculate the change potential from compare it to the approximation 0.1 and 0 to t dt Repeat the comparison for the interval from t - 0 to t-0.01. (Be sure to keep enough significant digits to resolve the...