Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Calculus Formulae Booklet, Exercises of Mathematics

Mathematics

Differential And Integral Calculus Formulae

Typology: Exercises

2018/2019

Uploaded on 11/16/2019

student_us
student_us 🇺🇸

1 document

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Absolute function f(x) =
1. -(x-c) if x
2. 0 if x = c
3. x-c if x
Prove Continuous at x = a of f(x)
1. f(a) exists. f(a) is define.
Any polynomial is continuous everywhere all x.
Any rational function is continuous where it is defined on its domain.
Basic Limit Evaluations at *
Limit at Infinity: Horizontal asymptotes
Find Vertical Asymptotes
1. Simplify the func. by common factors between numerator and
denominator.
2. Make the denominator =0 for x
3. x = a is the Vertical Asymptotes.
Limit of Trigonometric Functions
Miami Dade College -- Hialeah Campus
Definition of the number (when )
Slope; m
1. m > 0 positive
2. m < 0 negative
3. m = 0 Horizontal
4. m=Vertical = no slope
Derivatives and Rates of constant a slope of secant line (x+h, f(x+h)) a slope of tangent line (x , f(x))
= average rate of change or different quotient
pf3

Partial preview of the text

Download Calculus Formulae Booklet and more Exercises Mathematics in PDF only on Docsity!

Absolute function f(x) =

  1. -(x-c) if x
  2. 0 if x = c
  3. x-c if x Prove Continuous at x = a of f(x)
  4. f(a) exists. f(a) is define. Any polynomial is continuous everywhere all x. Any rational function is continuous where it is defined on its domain. Basic Limit Evaluations at * Limit at Infinity: Horizontal asymptotes Find Vertical Asymptotes
    1. Simplify the func. by common factors between numerator and denominator.
    2. Make the denominator =0 for x
    3. x = a is the Vertical Asymptotes. Limit of Trigonometric Functions Miami Dade College -- Hialeah Campus Definition of the number (when ) Slope; m
  5. m > 0 positive
  6. m < 0 negative
  7. m = 0 Horizontal
  8. m=Vertical = no slope Derivatives and Rates of constant a slope of secant line (x+h, f(x+h)) a slope of tangent line (x , f(x)) = average rate of change or different quotient

The slope of tangent line = m (of f(x) at x=a) = Velocity of f(x) as v (limit of difference quotient or Derivative of f(x) at x=a) An Equation of Tangent Line Use the given f(x)

  1. Find slope m
  2. Find f'( = m 3. y - ( x - ) --> to make y = ax + b form Differentiable at x Provided the limit exists. We say that the func. y = f(x) is differentiable at x Derivatives of y = f (x) y' = f'(x) = = Differentiable at a = continuous at a No differentiable the f(x) could be continuous or not No Limit, No differentiable No Differentiable corner discontinuous tangent line( m )=vertical f'(x) = y = p(x) = a polynomial degree n The Linear approximation = a tangent line approximation The Linearization of at a y = f (x) The differentials dy by using L x ’ x x-a) + f(a) The differentials dy by using L x ’ x x-a) + f(a) a tangent line but Find Approximate the function ( x of L (x) is 0 because 0.04 is closest to 0) L ’ ( x of L (x) is 0 because -0.015 is closest to 0)
  3. Constant Multiple Rule c f(x) = c f '(x)