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4-75.
  1. graph at right The graph of a function f(x) is given at right. Use the graph to evaluate the following limits. Homework Help ✎

    1. Where (if anywhere) does the derivative of f(x) not exist?

The limit does not exist, but y→+∞.

A limit is a predicted value (which sometimes differs from the actual function value). The prediction must agree from the left and the right.

What is the prediction from the right?

lim x→∞ and lim x→−∞ will reveal the equation of a horizontal asymptote, if there is one.

What is the prediction from the left?

Most of the time, the limit and the function value agree.

Look for cusps, endpoints, jumps, holes, and vertical asymptotes.