Introduction to Limits At Infinity Notes - Edubirdie

University:
York University
Course:
MATH 1013 | Applied Calculus I
Academic year:

2022
Views:

195

Pages:

1
Author:

Nick T.

Introduction to Limits at Infinity lim(x→∞) f(x) = L lim(x→-∞) f(x) = 2 lim(x→∞) f(x) = -3 Limits at Infinity of Quotients (4x^5 - 3x^2 + 3) / (6x^5 - 100x^2 - 10) ≈ 4x^5 / 6x^5 = 4/6 = 2/3 Focus on which terms are going to dominate the rest. f(x) = (x + 1) / √(x^2 + 1) lim(x→∞) f(x) = lim(x→∞) x / √(x^2) = x / |x| Which term dominates? lim(x→∞) (√(4x^4 - x) - √(x^4 + 3x^2)) / (4x - 1) = lim(x→∞) ((√(4x^4 - x) - √(x^4 + 3x^2)) / (4x - 1)) * ((√(4x^4 - x) + √(x^4 + 3x^2)) / (√(4x^4 - x) + √(x^4 + 3x^2)))) = lim(x→∞) (4x^4 - x - x^4 - 3x^2) / ((4x - 1)(√(4x^4 - x) + √(x^4 + 3x^2))) = lim(x→∞) (3x^4 - 3x^2) / ((4x - 1)(√(4x^4 - x) + √(x^4 + 3x^2))) = lim(x→∞) (3x^2(x^2 - 1)) / ((4x - 1)(√(4x^4 - x) + √(x^4 + 3x^2))) = 3/4

Related Documents

Introduction to Limits At Infinity Notes

Introduction to Limits At Infinity Notes - Page 1

of 1

New Documents from this Course

Chapter 3.3 Derivatives Of Trig Functions Notes

Chapter 3.3 Derivatives Of Trig Functions Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Chapter 3 On Differentiation Rules Notes

Chapter 3 On Differentiation Rules Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Chapter 2.6 & 2.3 on Continuity Notes

Chapter 2.6 & 2.3 on Continuity Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Derivatives and Rates Of Change Notes

Derivatives and Rates Of Change Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Part 2 Limits and Derivatives Chapter 2 Notes

Part 2 Limits and Derivatives Chapter 2 Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

The Product Rule Importance

The Product Rule Importance

York University MATH 1013 | Applied Calculus I

Lecture Note

Chapter 3.1 Class Exercise Notes

Chapter 3.1 Class Exercise Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Trig Limits Using Double Angle Identity Notes

Trig Limits Using Double Angle Identity Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Chapter 3.1 Power Functions Notes

Chapter 3.1 Power Functions Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Velocity Graph Notes

Velocity Graph Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Limits and Derivatives Chapter 2 Notes

Limits and Derivatives Chapter 2 Notes

York University MATH 1013 | Applied Calculus I

Lecture Note

Calculus on Function and Types of Functions Notes

Calculus on Function and Types of Functions Notes

York University MATH 1013 | Applied Calculus I

Lecture Note