1limits & Continuityap Calculus

by admin

2011-2012

Describe or draw a function, f(x), with the following characteristics:

Now 0/0 is a difficulty! We don't really know the value of 0/0 (it is 'indeterminate'), so we need another way of answering this. So instead of trying to work it out for x=1 let's try approaching it closer and closer.

Numerical Approach to Limits Example 1: Let f (x) = 2 x + 2 and compute f (x) as x takes values closer to 1. We first consider values of x approaching 1 from the left (x 1). We now consider x approaching 1 from the right (x 1). A handy tool for solving limit problems. Wolfram Alpha computes both one-dimensional and multivariate limits with great ease. Determine the limiting values of various functions, and explore the visualizations of functions at their limit points with Wolfram Alpha.

  • f(x) has domain (–∞,8)
  • f(x) has range (–∞,9)
  • f(4) = 0; f(5) = 0; f(7) = 0
  • The limit, as x approaches –∞, of f(x) equals 9
  • The limit, as x approaches 8 from the left, of f(x) equals –∞
  • f(–1) = f(–3); f(–1) > f(–2)
  • f(1) = 1
  • The limit, as x approaches 1, of f(x) is 4

One Solution (others possible but similar):

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Ap Calculus Limits And Continuity Quiz #1-a

Calculus

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