calculus worksheet 1 - eleanor roosevelt high school
TRANSCRIPT
Math Calculus Worksheet Chap 1: Limits and Their Properties Section: Name:
Mr. Lin
7
38 Theorem: The Squeeze Theorem If ℎ 𝑥 ≤ 𝑓(𝑥) ≤ 𝑔(𝑥) for all x in an open interval containing c, except possibly at c itself, and if lim!→! ℎ 𝑥 = 𝐿 = lim!→! 𝑔 𝑥 , then
_____________________ and ____________________.
39 Theorem: Two special trigonometric limits.
(1) Prove: lim!→!!"#!!= 1
Area of triangle ≥ Area of sector ≥ Area of triangle
___________ ≥ ____________ ≥ ______________. Multiply each expression by !
!"#! produces
___________ ≥ ____________ ≥ ______________.
Taking reciprocals and reversing the inequalities yields
___________ ≤ ____________ ≤ ______________.
Since cos(−𝜃) = ___________ and !"#(!!)(!!)
= _____________,
You can conclude that the inequality is valid for all
nonzero 𝜃 in the open interval ____________________.
Since lim!→! cos 𝜃 = ________ and lim!→! 1 = _________,
you can apply the Squeeze Theorem to conclude that
_____________________________________________.
(2) Prove: lim!→!!!!"#!
!= 0
40 Example: Find the limit: lim!→!!"#!!
.
41 Exercise: Find the limit: lim!→!!"#!!!
.
42 Example: Find the limit: lim!→!!"#!!!"#!!
.
43 Example: Find the limit: lim!→!!!!
!!!"#!!.
44 Example: Find the limit: lim!→!!!
!"#!!.
𝜃 𝜃 𝜃 1 1 1