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sketch x^x

username1192424

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(edited 6 years ago)

Reply 1

MathsNerd1

Original post by sangyoonknow

How do you sketch the negative part of the graph?

Moved to Maths section :smile:

Reply 2

Alchemise

When x<0, y values are non-existent

Reply 3

davros

Original post by Alchemise

When x<0, y values are non-existent

Really? What about x = -1? What about x = -2? Etc...

Reply 4

Hasufel

for negative integers (ONLY) - (x^x is complex for x not in Z^(-)), imagine twanging a ruler on a desk end. It gradually settles down to being parallel with the end.

That is something like the graph of x^x for negative x (integers only). Calculate each x^x for negative Integerers down to say, -5 and plot them. They will be single dots, alternating between +ve and -ve y values, gradually converging to zero as x approaches negative infinity (because the smaller the negative x value, the smaller (in magnitude) the y value. The function for x>0:

1) examine the behaviour as x-> infinity and as x approaches zero by using L`Hopital`s rule. (hint: set y= x^x, then take natural logs, set "ln(y)" equal to ln(x)/ 1/x and calculate limit.

2) look for a stationary point by taking logs and implicit differentiation (it`s ( (1/e), (1/e)^(1/e)) )

(edited 9 years ago)

Reply 5

TeeEm

Original post by Alchemise

You're an ignorant idiot and - bastard

0^0 = undefined and so we can't sketch further than 0 and <0

Although I agree with you on what the graph of x^x looks like I do not think this aggressive outburst is neither appropriate nor intelligent.

Reply 6

davros

Original post by Alchemise

******************
0^0 = undefined and so we can't sketch further than 0 and <0

Reported for abuse.

As Hasufel pointed out, there are a number of discrete points that can be plotted for x < 0 and a continuous smooth curve for x > 0.

If you can't be civil, stay off the Maths forum.