M119 2018 Fall Midterm

M119 2018 Fall Midterm

Assessment

Flashcard

Mathematics

12th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

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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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