28 topics
Calculus help, from limits to series
Calculus punishes a specific thing: knowing the rules but not which one applies. Students who can differentiate anything you hand them still freeze on an optimization problem, because the difficulty was never the derivative — it was setting up the equation and knowing what to do with the constraint.
Where students get stuck
Product, quotient, or chain rule — I pick the wrong one
Read the outermost operation. If the whole expression is two things multiplied, it is product rule. Divided, quotient rule. If it is one function fed into another — anything of the form (something)^n, sin(something), e^(something) — it is chain rule. Most hard derivatives are nested, so the real skill is applying this repeatedly from the outside in, not choosing once.
Optimization problems — I can differentiate but I can't set them up
The setup is always the same three lines and it is worth doing them in order every time. Write the quantity to be maximised or minimised. Write the constraint — the fixed budget, the fixed perimeter, the fixed volume. Use the constraint to eliminate one variable, so you are optimising a function of one variable, and only then differentiate. Students who stall here almost always tried to differentiate a two-variable expression.
Which integration technique?
In order. Does a substitution clean it up — is some function's derivative sitting there as a factor? If not, is it a product of two unrelated things, which is integration by parts? Is it a rational function, which is partial fractions? Does it contain a² − x² or similar, which is trig substitution? Trying them in that order costs less than staring at it, because substitution is both the most common and the cheapest to rule out.
I never know which convergence test to use
Look at what the terms are made of. Factorials or n-th powers means ratio test. A rational function of n means limit comparison against the p-series with the same degree difference. Alternating signs means the alternating series test. And always check first that the terms go to zero — if they do not, it diverges and you are done in one line. The test is chosen by the shape of the term, not by the chapter it appeared in.
What's covered
Calculus topics you can work through with a tutor, generate practice on, or turn into flashcards and a study plan.
Limits and continuity
- Limits graphically, numerically, and algebraically
- Indeterminate forms and algebraic manipulation
- One-sided limits and limits at infinity
- Continuity and the Intermediate Value Theorem
- The formal definition of a limit
Derivatives
- The derivative from first principles
- Power, product, quotient, and chain rules
- Trigonometric, exponential, and logarithmic derivatives
- Implicit differentiation and logarithmic differentiation
- Higher-order derivatives
Applications of derivatives
- Related rates
- Critical points, increasing and decreasing intervals
- Concavity, inflection points, and curve sketching
- Optimization
- The Mean Value Theorem
- L'Hôpital's rule
- Linear approximation and differentials
Integration
- Antiderivatives and indefinite integrals
- Riemann sums and the definite integral
- The Fundamental Theorem of Calculus
- u-substitution, integration by parts, partial fractions, trig substitution
- Improper integrals
Applications and series
- Area between curves
- Volumes by discs, washers, and shells
- Arc length and average value
- Differential equations and separation of variables
- Sequences, series, and convergence tests
- Power series, Taylor and Maclaurin series
Calculus questions
Does it cover AP Calculus AB and BC, or university calculus?
The topic list above spans both — AB and BC map onto it, and a first-year university Calculus I/II sequence covers the same ground with more emphasis on proof and series. Tell it which course you are in and it will match the depth and notation expected of you.
Can it show me the graph, not just the algebra?
Yes. The whiteboard sketches curves as it explains, which matters most for concavity, curve sketching and volumes of revolution — problems where the picture is genuinely half the answer and a list of steps is not enough.
I have to show my work for full marks. Does it teach the steps or just answer?
It writes out the steps as it goes and asks you to supply the next one. If you already have an attempt, you can hand it in and get told which line the error starts on and why — which is usually more useful than a correct solution you did not produce.
Can I get practice problems for one specific technique?
Yes. Narrow it as far as you like — 'integration by parts only', 'related rates with cones' — and it generates a fresh set with full worked solutions.
Stuck on calculus right now?
Talk it through out loud, share your screen, and watch it worked out step by step on a whiteboard.
Start free — no card