Tom N. answered • 06/24/19
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Strong proficiency in elementary and advanced mathematics
Use the limit quotient rule lim f(x)/g(x) as x goes to 0 and take the limit of the numerator first which gives 8 as x goes to 0. For the denominator cot(x) goes to ∞ as x goes to 0 so the limit of the original function is Limx→0 8/∞ which is 0.
Tom N.
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The cot x is cosx/sinx when x goes to 0 cosx goes to 1 and sinx goes to 0. So 1/0 is defined as infinity. Inifinity is a very large number and so dividing 8 by a very large number gives essentially 0 for a quotient. Another way to do the problem is to rewrite it as lim as x goes to 0 (x+8)sinx/cosx. When you take the limit you get 8*0/1 which gives 0. Hope this helps.
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06/24/19
Geoffry B.
That is a wonderful explanation! Cheers!
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06/24/19
Geoffry B.
Hi Tom, Thank you for the explanation. Could you explain why cot goes to inifnite and also 8/infinite=0?06/24/19