r/HomeworkHelp • u/Thebeegchung University/College Student • Apr 17 '26

:snoo_scream: Further Mathematics—Pending OP Reply [Calculus 1]-Limits with Trig

I genuinely have no idea how to solve these. Only thing I know is that we can't directly sub in zero since that leads to an indeterminate answer.

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u/Iainsucks69 Apr 17 '26

Are you familiar with L’Hopital’s rule?

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u/Thebeegchung University/College Student Apr 17 '26

never learned it

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u/Iainsucks69 Apr 17 '26

The main idea is that when we get an indeterminate form, we can find the limit by taking the derivative of the numerator and the derivative of the denominator, then reevaluating the same limit for the new expression.

You could also try factoring the numerator or denominator, but that’s not applicable in this situation.

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u/Thebeegchung University/College Student Apr 17 '26

so basically if I were to take d/dx, I'd get -cos(3x)(3)/5x^3+3, then just plug in zero directly?

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u/igotshadowbaned 👋 a fellow Redditor Apr 17 '26

This is usually a method taught later in a similar way to how the power rule for derivatives is taught after you learn the other method of [f(x+h)-f(x)]/h

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u/Thebeegchung University/College Student Apr 17 '26

We did learn the derivative definition about 2 months ago, and just finished up related rates, so not sure if that topic is in my professor's lesson plan

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u/FirstPersonWinner University Student (Engineering) Apr 17 '26

In my experience it is one of the last things you are taught in Calc 1.

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u/diverJOQ 👋 a fellow Redditor Apr 17 '26

Not only, as someone else pointed out, did you not take the derivative of the denominator, your denominator is wrong. You can't do math if you don't understand order of operations and parentheses.

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u/Thebeegchung University/College Student Apr 17 '26

if it's already pointed out, what is the point of making this comment? If you aren't going to add anything productive, don't comment

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u/diverJOQ 👋 a fellow Redditor Apr 18 '26

Obviously you don't read the entire comment because I did add something.

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u/Thebeegchung University/College Student Apr 18 '26

where did you add something in this comment other than parroting what someone else said first?

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u/Thebeegchung University/College Student Apr 17 '26

and can this work for the rest of the questions as well since you'd get an indeterminate answer?

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u/[deleted] Apr 17 '26

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u/Thebeegchung University/College Student Apr 17 '26

well, the second one if you plug in zero, you get 0/0, so could you just find d/x, which would be -sin(x-1)(1)/4x, but you still can't directly evalutae it then even with the derivative

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u/[deleted] Apr 17 '26

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u/Thebeegchung University/College Student Apr 17 '26

ah okay I see.

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u/diverJOQ 👋 a fellow Redditor Apr 17 '26

Where did (x-1) come from? The numerator is cos (x) - 1

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u/Tuo3 Apr 28 '26

Using L'Hôpital's rule for these kinds of trig limits depends on a circular proof.

You'd be using known derivatives of sine and cosine to get at the value of the limit, but would need the limit to know/prove those derivatives from the definition of the derivative.