# Study Guides for MATH 100 at University of British Columbia - Okanagan (UBC OKANAGAN)

UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 25: Derivative Test, Second Derivative, Inflection

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 24: Maxima And Minima

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture 23: Maxima & minima

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture 22: linear approximation and differentiation

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 18: Inverse Function, Binary Logarithm, Logarithm

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Math 100 lecture 8 inverse functions. Partial proof of the chain rule: =() = () , =() =( + ) (), = , 0. = . , 0 lim 0 = lim 0 . lim 0 the general formu
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 19: Inverse Trigonometric Functions, Inverse Function, Logarithm

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Math 100 lecture 19 derivative of inverse functions and implicit functions. = sin is not one-to-one, so an inverse function cannot be found. The line c
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Study Guide - Fall 2018, Comprehensive Midterm Notes - Thomas Robert Shannon Broughton, Trigonometric Functions, Graph Of A Function

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Math 100 lecture 1 diagnostic test & solutions: x = 2 is a root for the polynomial x3 x2 8x + 12. Find all of the roots of this polynomial by factoring
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 17: Quotient Rule, Product Rule

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Math 100 lecture 17 derivative of trigonometric functions. = 1 + = (1 +: what is (3. 2 is an exponential with base 2: 2 = (2) Now use the quotient rule
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 16: Power Rule, Quotient Rule

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Math 100 lecture 16 derivatives and exponential functions. Quotient rule: how to differentiate a quotient function like =()() () are differentiable, an
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 15: Third Derivative, Power Rule, Product Rule

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Math 100 lecture 15 derivative rules. Third derivative: the derivative of , written as . 4th derivative of =(): nth derivative of =(): 33 (2) = (2) = (
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 14: Constant Function

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Math 100 lecture 14 the derivative function & differentiation. The derivative of the function () for all values of when the limit exists is defined as.
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 13: Time 100

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Math 100 lecture 13 the derivative function. Examples for the derivative showing as the instantaneous rate of change: =() for the population of bacteri
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 12: Difference Quotient

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Tangent line at a point on a graph of a function, runs along the curve at that point. To find a line, you need a point and the slope. Since you already
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 8: Classification Of Discontinuities, Squeeze Theorem, Symmetric Function

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 9: Algebraic Solution, Asymptote, Intermediate Value Theorem

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Math 100 lecture 9 continuity on intervals. You can just plug in 3, then use limit laws, because the function is continuous (cid:4666)(cid:885) (cid:88
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 7: Squeeze Theorem, Horse Length

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Math 100 lecture 7 limits, part 4: multiply by conjugate, find a common factor on top and bottom. If the result of a limit is 00, you need to examine t
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 6: Indeterminate Form, Power Law, The Thirteen Chairs

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Math 100 lecture 6 limits, part 3 (cid:2922)i(cid:2923) (cid:3034)(cid:4666)(cid:4667) ,(cid:1858) lim (cid:1859)(cid:4666)(cid:4667) (cid:882) If lim
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Fall 2018 Lecture 5 - Negative number, Asymptote, Constant function

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Math 100 lecture 5 limits, part 2. Limits that do not exist: oscillating limits, different left and right sides. From the graph it is observed that if
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 4: Horse Length

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It was realized that the world can be understood by calculus. It can describe the changes in science, engineering, economics, etc. Although the logic b
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 3: List Of Trigonometric Identities, Linear Function, Floor And Ceiling Functions

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Math 100 lecture 3 functions pt. In order to use desmos for the greatest integer function, you can write floor(x) . The greatest integer function is al
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 1: Negative Number, Cube Root, Trigonometric Functions

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Math 100 lecture 1 diagnostic test & solutions: x = 2 is a root for the polynomial x3 x2 8x + 12. Find all of the roots of this polynomial by factoring
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture Notes - Lecture 2: Piecewise, Floor And Ceiling Functions

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An input goes in the fraction to get the output. For every input, there is only one output. If the domain is changed, the function is changed, even wit
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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture 7: 3.5. implicit differentiation

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Lecture 8: 3.6. logarithmic functions

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UBC OKANAGAN, UBC OKMATH 100Wayne BroughtonFall

## MATH 100 Study Guide - Fall 2018, Comprehensive Midterm Notes - Thomas Robert Shannon Broughton, Trigonometric Functions, Graph Of A Function

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Math 100 lecture 1 diagnostic test & solutions: x = 2 is a root for the polynomial x3 x2 8x + 12. Find all of the roots of this polynomial by factoring
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UBC OKANAGAN, UBC OKMATH 100AllWinter

## MATH 100 Exam Solutions Winter 2018: Quotient Rule, Chain Rule, Squeeze Theorem

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From the general definition of derivative, the derivative of (cid:1858)(cid:4666)(cid:1876)(cid:4667) at (cid:1853) is given by (cid:1858)(cid:4593)(ci
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UBC OKANAGAN, UBC OKMATH 100AllWinter

## MATH 100 Midterm: MATH100 Midterm 2009 Winter Solutions

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The limit at c+ and c- will different values as the function is defined differently at c and at value less than c. Appling limit we get: (cid:958)(cid:
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UBC OKANAGAN, UBC OKMATH 100AllWinter

## MATH 100 Exam Solutions Winter 2018: Squeeze Theorem, Asymptote, Negative Number

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Factoring out both numerator and denominator we get: the function (cid:1858)(cid:4666)(cid:1876)(cid:4667)(cid:3404)(cid:3)(cid:3051)(cid:3118)(cid:3)(
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UBC OKANAGAN, UBC OKMATH 100AllWinter

## MATH 100 Exam Solutions Winter 2018: Product Rule, Indeterminate Form, Squeeze Theorem

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From the general definition of derivative, the derivative of (cid:1858)(cid:4666)(cid:1876)(cid:4667) at (cid:1853) is given by (cid:1858)(cid:4593)(ci
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UBC OKANAGAN, UBC OKMATH 100AllWinter

## MATH 100 Exam Solutions Winter 2018: Hypotenuse, Power Rule, Product Rule

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[6 marks] using only the de nition of the derivative, and not the rules, nd f(cid:2) (x) for the. 1. function f (x) = x2 + 1. Solution: f(cid:2) f(cid:
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