Answer :

Final answer:

The limit of a constant is the constant itself, so the limit as x approaches 0 is 6512. For the second part of the question, a limit concerning an exponential function x n * e -x, requires the use of L’Hôpital's Rule, but is likely to be zero as x approaches zero from the left.

Explanation:

To evaluate the limits, we first need to know the function, and then the variable which approaches a certain value. For a function f(x), the limit as x approaches c is traditionally noted as lim_(x->c) f(x).

Given two scenarios:

1. lim_(x->0-) 6512: This case is straightforward as the limit of any constant is the constant itself, thus lim_(x->0-) 6512 = 6512.

2. lim_(x-> 0-) x n * e -x, where n is any positive integer: This limit is a bit more complex and requires the application of L Hopital's Rule..

However, at first glance, it seems the limit would reach zero because x n will converge to zero faster than e -x will approach infinity, as x approaches zero from the left side. But to be sure, it would need to be confirmed through L Hopital's Rule.

It's important to remember that each limit problem case requires a specific approach, depending on what you're given.

Learn more about exponential function here:

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