Glossary
One-line pointers; full intuition lives on each topic page.
Vectors & geometry (MATH 151)
- Vector / dot product — Appendix J toolkit used before limits in this section. →
Limits & continuity
- Limit — “what $f(x)$ approaches” as $x$ approaches $a$ (value need not equal $f(a)$). →
- Continuity — no jump/hole at $a$: limit exists, $f(a)$ defined, and they match. →
- Removable discontinuity — limit exists but $\neq f(a)$ or $f(a)$ undefined; “fillable hole.” →
Derivatives
- Derivative — instantaneous rate of change; slope of tangent; $f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. →
- Differentiable — derivative exists (implies continuity there). →
Theorems (Calc 1)
- IVT — continuous on $[a,b]$ hits every height between $f(a)$ and $f(b)$. →
- MVT — if $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$, some $c$ has $f'(c)=\frac{f(b)-f(a)}{b-a}$. →
- FTC — connects differentiation and integration; area rate is the height. →