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7. Let x > O. Draw the graph of f (x) xx. Use a derivative to find its minimum value. L'Hospital's Rule: If f and g are differentiable functions on an open interval that contains a, and the limits lim f(x) and lim g (x) both equal zero both equal co, then f(x) lim lim assuming the limit on the right side exists. There are several different types of indeterminate forms (shown below). L 'Hospital's Rule works successfully with all types, provided that the expression can be written in the form of a fraction. 00 8. Use L'Hospital's Rule to evaluate the following limits. sin x a) lim 1 cos x b) lim c) lim x In x