Question

How do you do this question?

Answer 1

Answer: C) 1

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One way is to graph the function f(x) = ln(x)/(x-1) and you'll see the curve slowly approach y = 1 when x approaches 1 from either side. Check out the attached image labeled "figure 1" for this graph.

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You can use a table to see this in action. See figure 2 (attached below as well).

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Another alternative is to use L'Hospital's rule. This is because we get the indeterminate form 0/0 after plugging x = 1 into the original function.

if y = ln(x), then dy/dx = 1/x

If y = x-1, then dy/dx = 1

So f(x) = ln(x)/(x-1) becomes (1/x)/1 = 1/x

If you plug in x = 1, you get 1/x = 1/1 = 1.

Regardless of which method you use, the limiting value is 1