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IndeterminateForms - min max For example Plot Sin x x-π π...

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MATH 191, Sections 1 and 3 Calculus I Fall 2007 Indeterminate Forms As we saw on Monday, sometimes we can’t really tell what a given limit might turn out to be, simply because it has a vexing indeterminate form , like “ 0 0 ,” or “ infty .” We’re about to develop a method of evaluating such limits, and a slew more like them. Before we do that, though, it might be nice to play around with Mathematica a little bit, to see how it can help us at least guess what some of these nasty limits might be. Working together, use the Mathematica command Plot to graph each of the following functions and see if you can determine the value of the given limit. Recall that the syntax for Plot is as follows: Plot [ name of function , { variable
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Unformatted text preview: , min , max } ]. For example: Plot [ Sin [ x ], { x ,-π , π } ] Hints : recall that the trig functions have to be capitalized at the beginning, and that the natural logarithmic function is called Log in Mathematica . Finally, be careful with order of operations! 1. lim θ → sin( θ ) θ 2. lim x → 1 ln( x ) x-1 3. lim x →∞ e x x 4. lim x →∞ e x x 2 5. lim x →∞ e x x 3 6. lim t → 3 + t + 3 t-3 7. lim x →∞ ln( x ) √ x 8. lim x →∞ ln( x ) x 1 / 4 9. lim θ → π-sin( θ ) 1-cos( θ ) 10. lim θ → π 2-tan( θ )( θ-π 2 ) 11. lim θ → π 2-sec( θ )-tan( θ ) 12. lim x →∞ x 1 /x 13. lim x → + ( cos( x ) ) 1 /x 2...
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