McGill University · AEMA 101

McGill AEMA 101 tutoring

Calculus 1: send your chapter so we can check whether we can help before you book.

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Course overview

AEMA 101 at Macdonald Campus develops limits, derivatives, antiderivatives and applications after a review of functions. Start with a rate and its meaning below. Send your chapter or a question, even if you haven’t started it, so we can confirm support before booking.

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AEMA 101 topics to review

Functions and graphsLimits and continuityDerivatives and differentiation rulesAntiderivativesApplications of rates of change

Common difficulties

Reasoning about limits
Applying the chain rule to layered expressions
Turning an applied question into a function

A rate has units and a time interval

In an original practice model, a tank’s volume is $V(t)=50+6t-t^2$ litres, where $t$ is the numerical time in minutes and $0\le t\le4$ . Find the average rate from minute 1 to minute 2 and the instantaneous rate at minute 1. Predict whether they should agree before calculating.

Hint: average and instantaneous ask different questions

Average rate divides the change in volume by the elapsed time. Instantaneous rate is the derivative at one time. Here the graph bends downward, so the rate is decreasing.

Read the two rates with their units

The volumes are $V(1)=55$ L and $V(2)=58$ L, so the average rate is $(58-55)/(2-1)=3$ L/min. Differentiating gives $V'(t)=6-2t$ L/min, so $V'(1)=4$ L/min. The rate starts at 4 and falls to $V'(2)=2$ L/min; an average of 3 is consistent with that change.

The derivative is a rate, not a volume. The average uses both endpoints; evaluating $V'$ at the starting time does not generally give that interval’s exact average.

Retry: what does a zero derivative mean?

Find the average rate from minute 2 to minute 3 and the instantaneous rate at minute 3. Is the tank empty at minute 3? Keep your conclusion within the model’s stated time interval.

Check the changed interval

Since $V(3)=59$ L, the average rate is $(59-58)/(3-2)=1$ L/min. The derivative at 3 is $V'(3)=0$ L/min. Volume is momentarily no longer increasing at this instant, but the tank contains 59 L. A zero rate does not mean a zero amount; this model makes no claim about times beyond minute 4.

For the calculation rules behind the rate, try the existing derivative-rule check. Your AEMA 101 section determines which applications to review.

How tutoring can help

Send a rate question, with or without an attempted calculation. If support is confirmed, your tutor can compare the secant rate over an interval with the tangent rate at one time, check what the result measures and ask you to interpret a zero derivative in a changed example.

Exam preparation for AEMA 101

Decide whether each rate question asks for an interval average or an instantaneous value, and label the units. Retry the tank example without the solution, explaining why a zero derivative does not mean zero volume. Mix in the other topics on your exam list; check antiderivatives by differentiating.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

Need help with AEMA 101?

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AEMA 101 · official course reference