Help me in maths limits

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Hedwigeeeee
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#1
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#1
Are we able to apply the sandwich theorem here? I tried to do so but it does not work… can anyone help me?
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the bear
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#2
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you can see how the curve behaves without using a theorem. as you move to the right along the x axis the y values increase in amplitude with positive and negative values. as you move to the left the e3x term causes the y values to approach zero, again with positive and negative values.
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mqb2766
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the bear has given the right answer.

Its worth noting the duffers answer that it would be impossible to conclude anything other than the -> 0 part, as youre not given the "intiial conditions" constants A and B so tending to +inf or - inf is impossible to determine, no matter what growing exponent (positive real, complex with pos real).
Last edited by mqb2766; 1 month ago
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Hedwigeeeee
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#4
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#4
Thank u guys but I am confused how to deal with the sin and cos parts,because they fluctuates between -1 and 1
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mqb2766
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#5
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(Original post by Hedwigeeeee)
Thank u guys but I am confused how to deal with the sin and cos parts,because they fluctuates between -1 and 1
That was the point the bear was trying to make.
exp(3x)*cos(4x)
Is fairly easy to interpret. Just sketch cos(4x), then imagine the +/-1 max/min values being multiplied by exp(3x), so the magnitude of the oscillations are increasing exponentially. So something like
https://www.desmos.com/calculator/iudewt5u9w
Ive changed the 3 and 4 values to make the graph easier to interpret (the exponential growth rate is slower). They correspond to "roots" s = 1/8 +/- i

exp(3x)*sin(4x) is similar, just a small shift along the x-axis and similar for their sum.
Last edited by mqb2766; 1 month ago
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