What is the value of displaystylelim_x ightarrow-3fracx^2-9x^2-2x-15 ?


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displaystylefrac34 Explanation: displaystylelim_x o-3fracx^2-9x^2-2x-15 By factoring out the numerator and the denominator, displaystyle=lim_x o-3fraccancelleft(x+3 ight)left(x-3 ight)cancelleft(x+3 ight)left(x-5 ight)=frac-3-3-3-5=frac-6-8=frac34 ...
equirecancel note that both the numerator và denominator evaluate khổng lồ 0 at x = -3. That means we have an indeterminate limit, which simply means more work needs khổng lồ be done. Factor ...
https://math.stackexchange.com/questions/197844/help-with-epsilon-delta-proof-of-lim-x-to-3-fracx2-x-6x2-9
HINT: fracx^2+x-6x^2-9-frac56=frac6x^2+6x-36-(5x^2-45)6(x^2-9)=fracx^2+6x+96(x^2-9)=frac(x+3)^26(x-3)(x+3)
You can see if you solve for x=1 that you get a fraction in the size of dfrac00 which is indeterminate. When you get into a situation lượt thích this you can apply L'Hôpital's rule - Wikipedia. ...
https://math.stackexchange.com/questions/1872290/proving-that-lim-x-to-2-fracx2-5xx22-1-using-the-epsilon-delta
Let epsilon>0 be given. We have to find a number delta>0 such that left|fracx^2-5xx^2+2+1 ight|
cảnh báo that lim_x o -3 frac(x^2-9)^2x^2+colorred6x+9 We can solve in this way lim_x o -3 frac(x^2-9)^2(x+3)^2=lim_x o -3 frac(x-3)^2(x+3)^2(x+3)^2=lim_x o -3 (x-3)^2=36
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left< eginarray l l 2 & 3 \ 5 & 4 endarray ight> left< eginarray l l l 2 & 0 và 3 \ -1 và 1 và 5 endarray ight>
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