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