
M119 2018 Fall Midterm

Flashcard
•
Mathematics
•
12th Grade
•
Hard
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14 questions
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1.
FLASHCARD QUESTION
Front
What is the Fundamental Theorem of Calculus?
Back
The Fundamental Theorem of Calculus links the concept of differentiation and integration, stating that if a function is continuous on the interval [a, b], then the integral of its derivative over that interval is equal to the difference in the values of the function at the endpoints: ∫[a,b] f'(x) dx = f(b) - f(a).
2.
FLASHCARD QUESTION
Front
Define a limit in calculus.
Back
A limit is a fundamental concept in calculus that describes the behavior of a function as its argument approaches a particular point. It is expressed as: lim (x -> c) f(x) = L, meaning that as x approaches c, f(x) approaches L.
3.
FLASHCARD QUESTION
Front
What is the derivative of a function?
Back
The derivative of a function at a point measures the rate at which the function's value changes as its input changes. It is defined as the limit of the average rate of change of the function over an interval as the interval approaches zero: f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h.
4.
FLASHCARD QUESTION
Front
Explain the concept of continuity in a function.
Back
A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. Formally, f is continuous at x = c if: 1) f(c) is defined, 2) lim (x -> c) f(x) exists, and 3) lim (x -> c) f(x) = f(c).
5.
FLASHCARD QUESTION
Front
What is an asymptote?
Back
An asymptote is a line that a graph approaches but never touches. There are three types of asymptotes: vertical (x = a), horizontal (y = b), and oblique (slant) asymptotes.
6.
FLASHCARD QUESTION
Front
Define a critical point in calculus.
Back
A critical point of a function occurs where its derivative is either zero or undefined. Critical points are important for finding local maxima and minima of the function.
7.
FLASHCARD QUESTION
Front
What is the difference between a definite and an indefinite integral?
Back
A definite integral computes the area under a curve between two specific points and results in a numerical value, while an indefinite integral represents a family of functions and includes a constant of integration (C), representing the antiderivative of a function.
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