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# Innite Discon tin uities In an innite discon tin uit the left and righ thand limits are innite they ma oth ositiv e oth gati e or one ositiv and one negativ e PDF document - DocSlides

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Inﬁnite Discon tin uities In an inﬁnite discon tin uit the left- and righ t-hand limits are inﬁnite; they ma oth ositiv e, oth gati e, or one ositiv and one negativ e. Figure 1: An example of an inﬁnite discon tin uit y: rom Figure 1, see that lim and lim Sa yin that limit is is iﬀe from sa ying that the limit do sn exist the alues of are hanging in ery deﬁnite as from either side. (Note that it’s not true that lim ecause and are diﬀeren t.) There are more things can learn from this example. First, sk etc the graph of dx it also has an inﬁnite discon tin uit at 0. Notice that the deriv ativ of the unction is alw ys negativ e. It ma seem strange to ou that the deriv ativ is decreas in as approac hes from the ositiv side while is increasing, but ery often the graph of the deriv ativ will lo ok nothing lik the graph of the original function. What the graph of the deriv ativ is sho wing ou is the slop of the graph of Where the graph of is not ery steep, the graph of lies close to the -axis. Where the graph of is steep, the graph of is far from Finally is an dd function and is an ev en function. When ou tak the -axis. The alue of slop es do wn ard. is alw ys negativ e, and the graph of alw ys the deriv ativ of an dd function ou alw ys get an ev en function and vice-v ersa. If ou can easily iden tify dd and ev en functions, this is go to hec

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Figure 2: op: graph of and Bottom: graph of our ork.

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IT OpenCourseWare http://ocw.mit.edu 18.01SC Single Variable Calculus Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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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Page 1

Inﬁnite Discon tin uities In an inﬁnite discon tin uit the left- and righ t-hand limits are inﬁnite; they ma oth ositiv e, oth gati e, or one ositiv and one negativ e. Figure 1: An example of an inﬁnite discon tin uit y: rom Figure 1, see that lim and lim Sa yin that limit is is iﬀe from sa ying that the limit do sn exist the alues of are hanging in ery deﬁnite as from either side. (Note that it’s not true that lim ecause and are diﬀeren t.) There are more things can learn from this example. First, sk etc the graph of dx it also has an inﬁnite discon tin uit at 0. Notice that the deriv ativ of the unction is alw ys negativ e. It ma seem strange to ou that the deriv ativ is decreas in as approac hes from the ositiv side while is increasing, but ery often the graph of the deriv ativ will lo ok nothing lik the graph of the original function. What the graph of the deriv ativ is sho wing ou is the slop of the graph of Where the graph of is not ery steep, the graph of lies close to the -axis. Where the graph of is steep, the graph of is far from Finally is an dd function and is an ev en function. When ou tak the -axis. The alue of slop es do wn ard. is alw ys negativ e, and the graph of alw ys the deriv ativ of an dd function ou alw ys get an ev en function and vice-v ersa. If ou can easily iden tify dd and ev en functions, this is go to hec

Page 2

Figure 2: op: graph of and Bottom: graph of our ork.

Page 3

IT OpenCourseWare http://ocw.mit.edu 18.01SC Single Variable Calculus Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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