Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...

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Find the limit of 3x^(2x) as x approaches to 0+.

That's not right, guys. Have you tried to graph it? With GeoGebra it looks like part of a parabola opening up with vertex at (0.36788, 1.43743).

If you put a point on the function and slide it toward 0 from the right it disappears at x = 0; so there’s a hole there. If you move it very close to 0 you get (0.00172952010749865, 2.93472308532316).

So the limit of 3x^(2x) as x approaches 0+ (from the right) is approximately 2.93472308532316.
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I found that we need to convert to logarithms and manipulate them into an indeterminate form in order to use L'Hopital's Rule.

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