Can someone explain what the notation h'(x)->infinity as x->0- means based on this graph?
I would expect it the line to be going straight up if h'(x) is approaching infinity when x approaches 0 from the left?
Is it to the right of 0 x is approaching infinity and to the left of 0 x approaches infinity? Of course, that's it, but have you ever seen it described this way? seems fucking returded
>>8196712
the superscript tells you which direction the limit approaches from
0+ means you're coming in from the right (more positive side)
0- means you're coming in from the left (more negative)
>>8196728
and so h'(x) going to infinity as x goes to 0- means that the graph approaches a vertical line as you approach 0 from the left
>>8196728
I get that, but
lim h(x) = infinity
x->0^-
doesnt make sense based on how the graph looks. as x approaches 0 from the left the limit is = 0
>>8196734
there's a difference between the limit of h(x) and the limit of h'(x)
the limit of h(x) as x goes to 0 from both sides is 0
the limit of h'(x) (the slope) is getting arbitrarily large though, as the slope goes from more horizontal away from 0, to upwards and vertical towards 0
>>8196734
and the graph is bounded between horizontal asymptotes at y=2,-2. Based on the statement i expect the limit to be going to infinity when x approaches 0 from the left or right, but instead x is going infinity (instead of y)
solution guide is wrong/email the instructor
>>8196740
because the slope is always positive?
>>8196741
it says positive infinity when you approach 0 from either direction, so you only really know how it behaves near 0 (better look like a vertical line asymptotically)
anywhere else you can draw whatever you want as long as its between -2 and 2
Okay, i got it. the notation still seems weird/unnecessarily confusing, but to i.e. to apply this to the first problem
when x is less than 2 the slop is between 0 and 1, or relatively horizontal, except when x approaches 2, where the slope is 1.
when x is greater than 2, the slope is between -1 and 0, or mostly horizontal with a slight down curve, except when x approaches 2 from the right, where the slope is -1.
ty
>>8196763
what exactly confuses you about the notation?
the +,- superscripts are useful for graphs where the limit is not the same from both sides
>>8196712
Well, it shows that h'(x) is not defined for x = 0. That's already known, though, because h(x) has a sharp turn (not smooth curve) at x = 0. Additionally, as you approach x = 0 from the left, h'(x) -> infinity (the slope of h(x) approaches a straight up and down line at x = 0). You see the same exact thing from the right.
>>8196712
>the line
Lrn2curve
