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Family of functions etc

  • Thread starter t_n_p
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  • #26
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You can draw it anyway that makes it clear to you. But most people would not say that there is a global max at -infinity since it's not really a point on the line. Similarly, no vertical asymptote there.
So no verticle asymptote, what about an arrowhead?

Also can you please confirm is this is correct.
lim -> -infinity = -infinity because x²e^(-ax) ->0 and
lim->infinity = 0 because x²e^(-ax) ->0

Thanks:tongue2:
 
  • #27
Dick
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So no verticle asymptote, what about an arrowhead?

Also can you please confirm is this is correct.
lim -> -infinity = -infinity because x²e^(-ax) ->0 and
lim->infinity = 0 because x²e^(-ax) ->0

Thanks:tongue2:
An arrowhead might be nice. I really don't know how you've been told to draw things. But limit -> -infinity=+infinity because both x^2 and e^(-ax) go to infinity. limit->infinity is zero because while x^2 goes to infinity e^(-ax) goes to zero faster.
 
  • #28
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Just one last question, graphically where would the points of inflexion (x=[2a±√(2)*a]/a²) lie?
 
  • #29
Dick
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Looking at your graph from left to right, it starts out being concave up (like the shape of U) switches to concave down around the maximum and then returns to concave up. The inflection points are were these changes happen. In practice it's easier to mark them on your graph first and then adjust your drawing to fit. As your max is at 2/a and sqrt(2) is about 1.4 there is one at about 3.4/a and one at about 0.6/a, right?
 

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