# For what values of x does the graph of #f(x)=e^(3x)# and #g(x)=x^2-2# have a horizontal tangent line?

The two functions do not share a tangent line (which seems to be what you are asking for).

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To find the values of x where the graph of f(x) = e^(3x) and g(x) = x^2 - 2 have a horizontal tangent line, we need to find the points where the derivative of each function is equal to zero.

The derivative of f(x) = e^(3x) is f'(x) = 3e^(3x). Setting this equal to zero, we get 3e^(3x) = 0. However, since e^(3x) is always positive, there are no values of x that make f'(x) equal to zero. Therefore, the graph of f(x) = e^(3x) does not have a horizontal tangent line.

The derivative of g(x) = x^2 - 2 is g'(x) = 2x. Setting this equal to zero, we get 2x = 0. Solving for x, we find x = 0. Therefore, the graph of g(x) = x^2 - 2 has a horizontal tangent line at x = 0.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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