- College prep∫Calculus📐
Taylor expansions at 0: the 6 essentials for prep classes
$e^x$, $\ln(1+x)$, $\sin$, $\cos$, $(1+x)^\alpha$, $\dfrac{1}{1-x}$ to order 3. The table that unlocks all 0-limits.
- High school∫Calculus📈
Product rule derivative: the « u'v + uv' » mnemonic
A little phrase to chant so you never mix it up again, and an example that clicks.
- High school∫Calculus🔓
The 5 logarithm properties to know 100%
$\ln$ turns products into sums, powers into products. Five formulas that unlock terminal-year calculus.
- High school∫Calculus⚠️
Spot an indeterminate form: the 4 classics
$\infty - \infty$, $\dfrac{0}{0}$, $\dfrac{\infty}{\infty}$, $0 \times \infty$. The 4 traps to catch so you never say « the limit exists » too fast.
- High school∫Calculus🚀
Limit at ±∞: keep only the dominant powers
At ±∞, only the highest-degree term matters. The rest gets crushed. A trick that simplifies 90% of polynomial and rational function limits.
- College prep∫Calculus♾️
Why the harmonic series diverges (but $\sum 1/n^2$ doesn't)
$\sum 1/n$ diverges, while $\sum 1/n^2$ converges. Elegant proof by grouping, plus the Riemann criterion.
- High school∫Calculus📋
The 8 derivatives to know by heart for the exam
A short table, memorizable in 10 minutes, that covers 90% of high school derivative calculations.
- High school∫Calculus🚀
Exponential beats all powers (at +∞)
No matter the power $x^n$, $e^x$ eventually surpasses it. The rule that settles all $e^x / x^n$ limits.
- High school∫Calculus∫
The antiderivatives to know by heart for the exam
Inverse of the derivatives table, plus a golden rule for the constant. A quick reference for integration.
- High school∫Calculus⛓️
Chain rule derivative: never get lost
$(f \circ g)' = f'(g) \times g'$. The mnemonic: « differentiate outside, keep inside, multiply by the derivative of inside ».
