This is an interesting problem.
What I would do first is try plugging in a somewhat large number, like 1000 for x.
It’s not infinity, but it’s large.
I removed the interior sets of parentheses since parentheses are implied in a fraction like that.
The expression then becomes a number a bit larger than 1, to an exponent of 2000.
If you go ahead and use a calculator, it becomes
That seems distinctly non zero to me!
So I tried a bigger number, x=1,000,000
It’s not immediately apparent what that value is. (you might try taking the natural log of this number though)
An approach which uses an early definition of e can help you solve this problem.
There is another approach you could use. One of the first steps is to put a base of e with the natural log of the expression. And we will need to use a Taylor Expansion later.
You may have seen the approximation that sinx ~ x for small values, there is a similar approximation for ln(1+x), 5/infinity qualifies as a small value. The first term of the Taylor Expansion is the most dominant for small values.
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