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Unformatted text preview: at the graphs of y = e x and y = x 2 on the same axes or use Intermediate Value Theorem). By comparing the graphs of y = e x , y =x , and y = x on the same axes (using the idea of the hint above), decide whether either of the functions g ( x ) or k ( x ) has vertical asymptotes. 3. Examine functions of the form h ( x ) = e ax for diﬀerent numbers a . Calculate the derivatives of h 1 ( x ) = e 2 x and h 2 ( x ) = ex by using the fact that e 2 x = e x · e x and ex = 1 e x . Do these agree with the general formula d dx e ax = ae ax ? Use the formula above and the simpliﬁcation ideas of this section to calculate the derivative of the function f ( x ) = ( e x + ex ) 2 e 2 x . 2...
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 Fall '08
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 Calculus, Derivative, Quotient Rule, Continuous function, horizontal tangent lines

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