MATH 2B Midterm: MATH 2B Midterm 2

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: All

Document Summary

Cross out incorrect scratch-work: no calculators or other forms of assistance are allowed. 1 x x2 4 dx: (15 points) determine whether the following improper integrals are convergent or divergent. Evaluate those that are convergent: z . 0 dz z2 + 3z + 2: (10 points) find the length of the curve f (x) = x3 + 1. 2 , 2: (10 points) determine whether each of the following statements is true or false. Brie y justify your answers: true/false: if {an} is decreasing and an > 0 for all n, then an is convergent, true/false: if f (x) g(x) and r . 0 f (x) dx also diverges: true/false: the integral z . 1 x dx converges: true/false: r 3. 2 dx: (15 points) determine whether each of the following sequences is convergent or divergent. If a sequence is convergent, nd its limit: an = n sin( 1 n , an = sin 1( 3n.