Figure 1 An example of an in64257nite discon tin uit y rom Figure 1 see that lim and lim Sa yin that limit is is i64256e from sa ying that the limit do sn exist the alues of are hanging in ery de64257nite as from either side Note that its not true t ID: 23792
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. limit is 1 is di erent from saying that the limit doesn't exist { the values of 1 x are changing in a very de\fnite way as x 0 from either side. (Note that it's ! 1 not true that lim = 1 because 1 x 1 is always negative. It may seem strange to you that the derivative is decreasing as x approaches 0 from the positive side while 1 is increasing, but very often the graph of the derivative will look nothing like x the graph 1 is steep, the graph of � 1 is far away from 2 x x Finally, is an odd function and � is an even function. When you take the x-axis. The value of � 1 x2 slopes downw 11 Figure 2: Top: graph of f(x) = and Bottom: graph of f0(x)= � x x 2 your work. 2