.MATH-1326-HW 04, 2023-02-11 1. Determine whether each improper integral converges or diverges. If it is convergent find the value a) dx -1 1 b) f 2xex dx Page 2 of 6 1 c) 3 dx x(lnx)2 d) 6xe-2x dx .MATH-1326-HW 04, 2023-02-11 Page 3 of 6 .MATH-1326-HW 04, 2023-02-11 2. The rate at which radioactive waste is entering the atmosphere at time t is decreasing and is given by Pekt,where P is the initial rate. Use improper integral fo Pe-kt dt to find the total amount of the waste that will enter the atmosphere, assuming P=50 & K=0.04. 3. Find the limit. Use l'Hospital's rule where applicable. a) lim 3x-2 x-8 X-8 Page 4 of 6 b) lim x-0 e ex-1+x -x-1-x) c) lim (xe-0.001x) X- .MATH-1326-HW 04, 2023-02-11 Page 5 of 6 d) lim (In (x+1)) x0 .MATH-1326-HW 04, 2023-02-11 lim (ev) e) lim Page 6 of 6