Math 101: Homework 3
Due Friday. Total: 30 points.
Name:
  1. 1.
    Compute ∫0πsin⁡x dx\displaystyle \int _0^{\pi } \sin x \, dx.  (5 points)
  2. 2.
    Solve the system  (10 points)
    x+y=3,2x−y=0. \begin{aligned} x + y &= 3, \\ 2x - y &= 0. \end{aligned}
  3. 3.
    Prove that 2\sqrt {2} is irrational.  (10 points)
  4. 4.
    True or false? Give a reason.  (5 points)
    1. (a)
      Every continuous function is differentiable.
    2. (b)
      ∑n≥11/n\sum _{n \ge 1} 1/n converges.