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Help me in maths limits
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Hedwigeeeee
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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?
Last edited by Hedwigeeeee; 5 months ago
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the bear
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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).
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; 5 months ago
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Hedwigeeeee
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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
Last edited by Hedwigeeeee; 5 months ago
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mqb2766
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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
Thank u guys but I am confused how to deal with the sin and cos parts,because they fluctuates between -1 and 1
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; 5 months ago
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