MATH 220-1
Written Homework 1
Fall 2019
• Work on these exercises in groups as directed by your teaching assistant.
• Solve these exercises and carefully write complete solutions on separate sheets of paper.
Follow the format requirements for written homework in the course policies on Canvas.
• Prepare a cover sheet for this assignment and staple it to the front of your written
solutions. Cover sheets are available from your teaching assistant and on Canvas.
• Submit your solutions to your instructor at the beginning of class on Friday, October 11.
1. Use the Sandwich Theorem to show that
1
lim x sin
= 0.
x→0
x
2
Show all of your work. Explain your reasoning in complete sentences.
2. Find δ > 0 such that for each x satisfying 0 < |x − 5| < δ,
√
x − 1 − 2 < 0.1.
Justify your answer.
3. Use the precise definition of a limit to prove that
lim (3x − 5) = 1.
x→2