limit X tends to infinity 2x^2+5x-2/x+7
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Answer:
Lim as x approaches inifinity of (5x^2 + 3x) /2x^2. How do we find the limit of this?
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Liam Hernon
Updated 4 years ago
Begin by noting that the limit, in its current form, is indeterminate. That is, if you were to 'sub in' infinity, you would have infinity/infinity, which is indeterminate.
The 2 most common ways to deal with limits in indeterminate forms are L'Hopital's rule or factorisation/polynomial long division. In 99.9% of cases, the former method is by far the easier method.
I will therefore use L'Hopital's rule to solve this problem.
L'Hopital's rule tell us that if the limit of a quotient assumes the indeterminate form 0/0, or infinity/infinity, then we can differentiate both the numerator and the denominator until the limit takes on a determinate form.
I begin by setting f(x)=g(x)h(x) , where g(x)=5x2+3x , and h(x)=2x2 .
As stated above, the limit is indeterminate:
L=limx→∞f(x)=g(∞)h(∞)=∞∞
I then take successive derivatives of both g(x) and h(x) until the limit assumes a determinate form:
L=g′(∞)h′(∞)=∞∞
L=g′′(∞)h′′(∞)=104=52 .
Therefore the limit is 52