Solutions from my first Calculus 1 exam

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Опубликовано:

23 сен 2024

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Комментарии : 30

@Alan-zf2tt 14 часов назад

Well - all I can say is: this is an excellent piece of work! Turning an exam into a test is one thing. Turning an exam into a learning experience is another. Cross linking with a bit of number theory (technically not essential as the event can also be explained by hand waving cyclical rotations) is ... speechless Your students are very fortunate people Michael. You are a great mathematician and a great educator Rock Star >

@ytdiegus 16 часов назад

I'd love a complete calculus course in MathMajor 🤓

@aweebthatlovesmath4220 19 часов назад

Fun questions prof penn!! Not making it too complicated for no reason i like it.

@martinkausoh1386 16 часов назад

Regarding question 6: it is easy to see that 1424 is a multiple of 4 so 1423 is 3 Mod 4. Division with remainder is .....😂

@markcrawford7483 15 часов назад

When looking for the remainder after dividing by 4, one only needs to look at the last two digits. This is do to the fact that any multiple of 100 is divisible by 4.

@stephenhamer8192 15 часов назад

Easy-peasy, except Q2 [esp. part c)] Somebody above has complained about about the curve-sketching Q. I can't agree with their low estimate of value. Curve-sketching is a really valuable activity, one encouraging students to concretise and _specialise_ their ideas about limits near points, continuity and differentiability. Also, this type of question is very "open", with a zillion "right" answers - and not merely computational / algorithmic Correction: easy-peasy, except Qs 1 + 2 [esp. part c) of Q2]

@CTJ2619 14 часов назад

you are an excellent math instructor - I taught for many years (math)

@CTJ2619 14 часов назад

i enjoyed you diff eq class you put together a while back

@Happy_Abe 4 часа назад

@14:25 we can’t cancel them out for g(x) since it’s not defined when x=-1 but for the derivative we can since the derivative is a limit

@Jack-e7i8s 15 часов назад

lim as x -> 0 of sin(ax)/sin(bx) = a/b, multiply that by cos(0) will get a/b

@ScienceTalkwithJimMassa 7 часов назад

Surprised to not see any find the equation of tangent line to the curve f(x) at point (a, b) question.

@shlokjajoo5760 6 часов назад

could u please make a video on the summation of sin^3n/n as n gors to infinity

@lisandro73 12 часов назад

Nice exam, for the ones who had studied is quite easy, to the ones who hadn't is hard

@dayingale3231 13 часов назад

Is this really a calc 1 exam? I find it supereasy, mine was a nightmare

@miraj2264 18 часов назад

For question 4 (namely 4b), I'd also ask what's the domain where the derivative exists. This is to emphasize that the simplification makes using quotient rule easier, but it's not the full story. I'd be curious if any students looked at 4b and simplified (x-1)/(2x+1) as [.5(2x+1) - 1.5]/(2x+1) = .5 - 1.5/(2x+1) in order to avoid quotient rule. I'm guessing they didn't just because you don't normally think about rewriting the numerator in terms of the denominator until after you start doing partial fraction qs.

@bobh6728 6 часов назад

It’s been too long since I took calculus, so is problem 4b differentiable at x=-1 even though it isn’t continuous. If it isn’t then the answer given is not correct.

@slavinojunepri7648 5 часов назад

g(x) is not differentiable at x=-1 and x=-1/2 because it is undefined at these values. Therefore g'(x) exists in the entire real line, except these values.

@picrust314 15 часов назад

Is there a pdf so one could have A go at it before watching?

@ISuperI 18 часов назад

wonderful exam questions not too crazy but also not just apply blindly definitions

@gp-ht7ug 17 часов назад

I would have passed it. Honestly I hate the ε test

@demenion3521 17 часов назад

i sense hermite polynomials in question 6, even though completely unnecessary connection here ^^

@Alan-zf2tt 14 часов назад

It is good to do things that way I think.

@firstname4337 16 часов назад

#1 is why i hated calculus class -- sketch this random graph -- why ? what's the point ??? give me an actual application -- of course this wasn't any different than most elementary and per-requisite courses either

@markcrawford7483 15 часов назад

It is not about applications at this level. I believe this question is designed to gauge how well his students understand the graphical interpretation of limits.