General Mathematics · 2nd secondary · First Term

Limits — Limit of a function at infinity

About this lesson

This unit focuses on the concept of the limit of a function at infinity. It begins with an activity using a computer program to graph the function f(x) = 1/x for x > 0, showing that as x increases towards infinity, f(x) approaches zero. The unit then presents basic rules for finding limits at infinity, such as the limit of a constant is the constant, and the limit of 1/x^n (where n is a positive number greater than 1) is zero. It explains that algebraic solutions involve techniques like factoring out the highest power of x and dividing numerator and denominator by the highest power in the denominator. The text includes worked examples and exercises for finding limits of polynomial and rational functions at infinity, with a note that the limit behavior depends on the degrees of the numerator and denominator. The unit also mentions that graphical solutions can be used to check results. By the end, a student should be able to find limits at infinity using algebraic and graphical methods, and understand the rules for polynomial functions.

Main topics in this lesson

  • Limit of a function at infinity
  • Algebraic solution for limits at infinity
  • Graphical solution for limits at infinity
  • Rules for limits of polynomial functions at infinity

Key terms and vocabulary

  • Limit of a function at infinity
  • Infinity
  • Algebraic solution
  • Graphical solution
  • Polynomial functions
  • Rational functions
  • Degree of numerator
  • Degree of denominator

Questions and answers on Limits — Limit of a function at infinity - practice and revision

Multiple choice questions on this lesson in General Mathematics for 2nd secondary, First Term, with practice exercises for revision and exam preparation.

1

ما قيمة نهاية الدالة f(x) = (6x^2 + 1)/(3x^2 + x) عندما تقترب x من ما لا نهاية؟

  • 1 6
  • 2 3
  • 3 2
  • 4 0
2

ما قيمة نهاية الدالة f(x) = x^2 + 3x عندما تقترب x من ما لا نهاية؟

  • 1 0
  • 2 3
  • 3 ما لا نهاية
  • 4 غير معروفة
3

ما قيمة نهاية الدالة f(x) = (x + 1)/(x - 1) عندما تقترب x من ما لا نهاية؟

  • 1 1
  • 2 -1
  • 3 0
  • 4 ما لا نهاية
4

ما قيمة نهاية الدالة f(x) = (5x^3 + 2x)/(x^3 + 1) عندما تقترب x من ما لا نهاية؟

  • 1 5
  • 2 2
  • 3 1
  • 4 0
5

ما قيمة نهاية الدالة f(x) = 2/(x^3) عندما تقترب x من ما لا نهاية؟

  • 1 2
  • 2 1
  • 3 0
  • 4 غير معروفة
6

ما قيمة نهاية الدالة f(x) = (x^2 + 1)/(x^3 + 2) عندما تقترب x من ما لا نهاية؟

  • 1 1
  • 2 0
  • 3 2
  • 4 ما لا نهاية

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