MATH 141: Test #2 Fall 2017 This examination contains 5 exercises on 5 pages and lasts 1h15. A formula sheet is attached on the last page. Please carefully justify your answers so that you may receive full credit. Exercise 1 Calculate the following limits. ln (15x) x 23x (a) lim (b) lim x0 cos (17x) 1 e25x 25x 1 Exercise 2 Evaluate the following improper integrals. If an integral diverges, determine whether it goes to , , or neither. Z + dx (a) dx 2+4 x Z (b) 0 3 ln 2 3x 3 x \u0001 dx Exercise 3 Find the tangent line to the parametric curve given by \u001a x = t5 4t3 , y = t2 at t = 2. Exercise 4 Find the length of the following curve, using the formula L = Rbp (dx/dt)2 + (dy/dt)2 dt. a x = 8t 43 + t 23 , t (2, 4) . 16 y = t 3 Exercise 5 Determine the area of the inner loop of r = 1 + 2 sin