Use your graphing calculator to evaluate limit as x goes to infinity of x^(1/2x)
I graphed it but couldn't figure out the limit.
Answers:
1) 1
2) e/2
3) pi
4) 0
is that x^[ 1/(2x) ] ?
if so then anything ^0 = 1
and on my calculator
10,000^(1/20,000) = 1.000460623
To evaluate the limit as x approaches infinity of x^(1/2x), you can use your graphing calculator's numerical approximation capabilities. Follow these steps to get the answer:
1. Turn on your graphing calculator and make sure it is in function evaluation mode.
2. Enter the expression x^(1/2x) into the calculator.
3. Instead of entering a specific value for x, we want to see what happens as x approaches infinity. To represent infinity on many calculators, you can use a very large number. Let's use a number like 10,000.
4. Plug in 10,000 for the x in your expression, x^(1/2x), and press enter.
5. Take note of the result it gives you.
The answer should be one of the following options: 1, e/2, pi, or 0. By performing the steps above, you can enter a large number, such as 10,000, for x and see if the expression converges to one of the given answer choices. If it does, then that is the limit as x approaches infinity. If it doesn't, then the limit does not exist.
Remember, this is just an approximation using numerical methods. To obtain a more rigorous proof of the limit, you would need to use techniques from calculus.