Calc. Chapter 2 Review

Calc. Chapter 2 Review

Assessment

Flashcard

Mathematics

11th Grade - University

Practice Problem

Hard

Created by

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the limit?

Back

The limit is the value that a function approaches as the input approaches a certain point. In this case, the limit is 20.

2.

FLASHCARD QUESTION

Front

Which of the following best describes the continuity at x = 0?

Back

Continuous: A function is continuous at a point if the limit as x approaches that point equals the function's value at that point.

3.

FLASHCARD QUESTION

Front

Find the vertical asymptote(s) of the function f(x) = (2x)/(x^2 - 1).

Back

The vertical asymptote is x = -2, where the function is undefined.

4.

FLASHCARD QUESTION

Front

Consider the function f(x) = (2x)/(x^2 - 1). Prove/disprove continuity at x = -5 using definition notation.

Back

lim f(x) as x→-5 = f(-5): The function is continuous at x = -5.

5.

FLASHCARD QUESTION

Front

Find the one-sided limit of f(x) = (2x)/(x^2 - 1) as x approaches 1 from the left.

Back

The one-sided limit exists and is -∞.

6.

FLASHCARD QUESTION

Front

Define continuity at a point.

Back

A function is continuous at a point if: 1) f(c) is defined, 2) lim f(x) as x approaches c exists, and 3) lim f(x) as x approaches c = f(c).

7.

FLASHCARD QUESTION

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining it appropriately.

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