Calculus Vocabulary
Grade 12 · Math · Flashcards
Master essential calculus terminology covering limits, derivatives, integrals, and related concepts.
Flashcards
- Derivative
- The instantaneous rate of change of a function; the slope of the tangent line at a point. f'(x) = lim(h→0) [f(x+h)-f(x)]/h.
- Integral
- The antiderivative of a function; also represents the signed area under a curve. Denoted ∫f(x)dx.
- Limit
- The value a function approaches as its input gets arbitrarily close to a specified value.
- Continuity
- A function is continuous at x=c if f(c) is defined, the limit exists, and both are equal.
- Differentiation
- The process of finding a derivative using rules such as power rule, chain rule, and product rule.
- Chain Rule
- d/dx[f(g(x))] = f'(g(x)) · g'(x). Used to differentiate composite functions.
- Product Rule
- d/dx[u·v] = u'v + uv'. Used when differentiating a product of two functions.
- Fundamental Theorem of Calculus
- Links differentiation and integration: if F is an antiderivative of f, then ∫[a to b] f(x)dx = F(b) - F(a).
- Critical Point
- A point where f'(x) = 0 or f'(x) is undefined; potential location of a local maximum or minimum.
- Inflection Point
- A point where the concavity of a function changes; f''(x) = 0 or changes sign there.
- Riemann Sum
- An approximation of the area under a curve using rectangles; the basis for the definite integral.
- Antiderivative
- A function F(x) whose derivative is f(x). Written F(x) = ∫f(x)dx + C, where C is a constant.
- Concavity
- Describes whether a curve bends upward (concave up, f''>0) or downward (concave down, f''<0).
- Asymptote
- A line that a curve approaches but never reaches; vertical asymptotes occur where a function is undefined.
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