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Example 2 Evaluate

Example 2 Evaluate Solution Observe that direct substitution of x=  into this limit produces the indeterminate form Hence we can apply L’Hopital’s Rule to evaluate this limit L :

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Example 2 Evaluate

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  1. Example 2 Evaluate Solution Observe that direct substitution of x= into this limit produces the indeterminate form Hence we can apply L’Hopital’s Rule to evaluate this limit L: If L  0, then we can divide the preceding equal by L to obtain 1 = 1/(ln 7) and ln 7 = 1. However, this statement is false. Hence L must equal zero. There is a problem with argument: it assumes that the limit L exists and equals a number. So we try an alternate argument which uses the definition of 7xas exln 7: Let u = x(ln 7 – 1). Then u goes to  when x goes to  because ln 7 – 1 > 0. Thus

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