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# (a) Show that the function defined by $f(x) = \left\{\begin{array} (e^{-1/x^2} \text{ if } x \not= 0 \\0 \text { if } x = 0 \end{array}\right.$is not equal to its Maclaurin series.(b) Graph the function in part (a) and comment on its behavior near the origin.

## a. see work for answerb. see work for graph

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the problem is showed that is a function they find it by blacks. Is they got e tunic to one on back square. Artifacts is not equal to zero. And the payroll. If axe instinct of zero is not in culture, it's Michael our Siri's. For a first, let's look at curative Lux two. You need to negative one over X toya hams. Two over. Ax killed. If Max is not, he can shoot zero and we can see that limit X from my axe goes to zero as he can't you, Cyril. So half half ex prom is they go to interconnected one of our square hams to overtax Killed. If axe is not zero and at one axe is he going to zero? It's degenerative and see much zero. Similarly, for second, which is called you to connective won over explainer times two over X Cube square plus two times connective three over access to the problem off. Or if X is not zero, my act is equal to zero we can find the limit of this function is equal to zero. What act goes to zero. So you win light. Why is equal to one over axe we can find that and preventive is ours too, He Conectiv. Why square hands some function about wine? Yeah, why is a phenomenal about what? And we have so here. This is accident, knotty or zero, and we have the limit. Why cause too fine Aunty eat connective y square Cam's some phenomenal, but why it's always equal to zero. It's over half were expensive. Zero and conservative is a go to cereal over half, So Michael are in Siri's off the function for wax. By definition, this is Echo two, some from zero to infinity. It's up and relative serial over Factorial axe to end, which is equal to zero things. The answer Votive at zero is always zero zero is a McLaren Siri's of the function apple backs so half are in axe is always equal to I need to connect one over X koi. If X is not equal to zero, this's a bearer bond for any end. So the limit. I'm Max. My aim goes to fine aunty. It is because to eat connected one over x squared if X is not equal to zero, So this is not equal to zero for any non zero number. So the function. It's not a country. It's my Clarence Siri's. Yeah, a part of B. Graf, the function part, eh? And the comment on its behavior nears raging. So that's the look. I was a graph of the function four blocks, so we can Samir a region value of function. It is almost zero. It's one of our small.

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