MTH 161 Study Guide - Fall 2018, Comprehensive Midterm Notes - Trigonometric Functions, Tanx, Squeeze Theorem
12 Oct 2018
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Department
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MTH 161
MIDTERM EXAM
STUDY GUIDE
Fall 2018
MTH 161 lec 1
Interval notation
ex)
25≤x≤28 = [25,28]
16<x≤21= (16,21]
−2<x<2 = (-2,2)
16≤x<21 = [16,21)
- Endpoints of intervals: If an endpoint is included, then use [ or ]. If not, then use ( or ).
For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7].
-Infinite intervals: For infinite intervals, use Inf for ∞ (infinity) or -Inf for -∞ (-
Infinity). For example, the infinite interval containing all points greater than or
equal to 6 is expressed [6,Inf).
- Unions of intervals: If the set includes more than one interval, they are joined using the
union symbol U. For example, the set consisting of all points in (-3,7] together with all
points in [-8,-5) is expressed [-8,-5)U(-3,7]. All sets should be expressed in their simplest
interval notation form, with no overlapping intervals.
- Empty intervals: If the answer is the empty set, you can specify that by using braces with
nothing inside: { }
- Special symbols: You can use R as a shorthand for all real numbers. So, it is equivalent to
entering (-Inf, Inf).
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- Set notation: You can use set difference notation. So, for all real numbers except 3, you
can use R-{3} or (-Inf, 3)U(3,Inf) since they are the same. Similarly, [1,10)-{3,4} is the
same as [1,3)U(3,4)U(4,10).
- One point intervals: When an interval contains only one point, enter it as a one point set
such as {3} or as a closed interval such as [3,3].
{x|x≠0,±1}{x|x≠0,±1}
Equals to (-inf,-1)U(-1,0)U(0,1)U(1,inf) using interval notation
Ex)
x≤3 and x≤−2: (-Inf,-2]
x≥−1and x≥14:[14,inf)
EX) Solve the following inequality.
−3≤5(x−5)≤20 : [22/5,9]
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Document Summary
Endpoints of intervals: if an endpoint is included, then use [ or ]. For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7]. In nite intervals: for in nite intervals, use inf for (in nity) or -inf for - (- For example, the in nite interval containing all points greater than or equal to 6 is expressed [6,inf). Unions of intervals: if the set includes more than one interval, they are joined using the union symbol u. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed [-8,-5)u(-3,7]. All sets should be expressed in their simplest interval notation form, with no overlapping intervals. Empty intervals: if the answer is the empty set, you can specify that by using braces with nothing inside: { } Special symbols: you can use r as a shorthand for all real numbers. So, it is equivalent to entering (-inf, inf).
