Definition of a limit

lim (x -> a) f(x) = L iff lim (x -> a-) f(x) = L and lim (x -> a+) f(x) = L

lim (x -> a) [f(x) ± g(x)]

lim (x -> a) f(x) ± lim (x -> a) g(x)

lim (x -> a) [f(x)g(x)]

lim (x -> a) f(x) * lim (x -> a) g(x)

lim (x -> a) [f(x)/g(x)]

lim (x -> a) f(x) / lim (x -> a) g(x), provided lim (x -> a) g(x) ≠ 0

Definition of continuity

A function f is continuous at x = a iff (1) f(a) exists, (2) lim (x -> a) f(x) exists, (3) lim (x -> a) f(x) = f(a)

line x=a if lim x->a +/- f(x) = +/-infinite

y=a if lim x-> +/- infinite f(x) = a

ln^d a < x^c < x^c ln^d < x^c+d < a^x < x! < x^x

lim x-> ∞ g(x)/f(x) = 0 lim x-> ∞ f(x)/g(x) = ∞

1. if f is continuous on closed interval (a,b) 2. then it has absolute max and absolute min on interval (a,b)

Definition of critical points

Critical point of f is a #c (x-value) such that 1. f'(c) = 0 OR f'(c) DNE

Candidates for extreme values on closed interval

1. find y-values of critical points in interval (a,b) 2. find y-values of endpoints, a and b 3. largest y-value = max, smalled = min

there exists a #cIf f continuous on (a,b) + differentiable on (a,b) Then there exists a #c b/t a and b such that f'(c) = f(b)-f(a)/b-a slope of tangent = slope of secant at some point b/t a + b

If f continuous on (a,b), differentiable on (a,b) and f(a)=f(b), Then there is atleast one #c on (a,b) such that f'(c) = 0

relative/local min/maxes must occur at critical points

1st derivative test for relative extrema

f(c) must exist 1. if f' changes from + to - at c, then f(c) = relative max 2. if f' changed from - to + at c, then f(c) = relative min 3. if f' doest change signs at c, then f(c) neither max/min

point on f graph where concavity of f changes

functio f has inflection point at (c,f(c)) if

1. f'' changes signs at x=c 2. f'' = 0 where f'' DNE

2nd deriv test for relative extrema

given f'(c) = 0, 1. if f''(c)<0 = max 2. if f''(c)>0 = min 3. if f''(c) = 0, test inconclusive

Mathematical Concepts and Formulas

Flashcard

•

Mathematics

•

12th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF.TF.A.4, HSF.TF.C.9, HSF.TF.A.2

Standards-aligned

Ash Udgirkar

Used 25+ times

FREE Resource

Student preview

58 questions

Show all answers

FLASHCARD QUESTION

Front

sin(x)/cos(x)

Back

tan(x)

Tags

CCSS.HSF.TF.A.4

FLASHCARD QUESTION

Front

cos(x)/sin(x)

Back

cot(x)

Tags

CCSS.HSF.TF.A.4

FLASHCARD QUESTION

Front

sec(x)

Back

1/cos(x)

Tags

CCSS.HSF.TF.A.2

FLASHCARD QUESTION

Front

csc(x)

Back

1/sin(x)

Tags

CCSS.HSF.TF.A.2

FLASHCARD QUESTION

Front

sin^2(x) + cos^2(x)

Back

FLASHCARD QUESTION

Front

sec^2(x) - tan^2(x)

Back

FLASHCARD QUESTION

Front

2sin(x)cos(x)

Back

sin(2x)

Tags

CCSS.HSF.TF.C.9

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

52 questions

Biología Celular y Procesos Metabólicos

Flashcard

•

12th Grade

50 questions

Tiền tệ Chương 1

Flashcard

•

50 questions

العربية للمبتدئين

Flashcard

•

University

44 questions

negocios hijos de su puta madre

Flashcard

•

12th Grade

44 questions

Leap 2 Chapter 8 Vocabulary

Flashcard

•

12th Grade

44 questions

Media B1 Flashcards adaptive 40Q

Flashcard

•

12th Grade

50 questions

Ethics Miterms

Flashcard

•

University

Popular Resources on Wayground

8 questions

Spartan Way - Classroom Responsible

Quiz

•

9th - 12th Grade

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

14 questions

Boundaries & Healthy Relationships

Lesson

•

6th - 8th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

3 questions

Integrity and Your Health

Lesson

•

6th - 8th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

9 questions

FOREST Perception

Lesson

•

20 questions

Main Idea and Details

Quiz

•

5th Grade

Discover more resources for Mathematics

25 questions

Logos

Quiz

•

12th Grade

14 questions

Making Inferences From Samples

Quiz

•

7th - 12th Grade

23 questions

8th grade math unit 5B Perfect Squares and Cubes

Quiz

•

6th - 12th Grade

15 questions

Exponential Growth & Decay Practice

Quiz

•

12th Grade

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

10 questions

Quadratic Regression Practice

Quiz

•

7th - 12th Grade

20 questions

Triangle Congruence Statements Quiz

Quiz

•

9th - 12th Grade

20 questions

5.1 Characteristics of Exponential Functions Lesson Check

Quiz

•

9th - 12th Grade