Limits and Continuity Quiz

Limits and Continuity Quiz

University

10 Qs

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Limits and Continuity Quiz

Limits and Continuity Quiz

Assessment

Quiz

Mathematics

University

Practice Problem

Medium

Created by

m g

Used 2+ times

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the definition of a limit in calculus?

The average value of a function

The value that a function or sequence approaches as the input or index approaches some value.

The lowest value of a function

The highest value of a function

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

State the limit definition of continuity at a point.

The limit definition of continuity at a point states that a function f(x) is continuous at a point c if the limit of f(x) as x approaches c exists, the function is defined at c, and the limit is equal to the value of the function at c.

The limit definition of continuity at a point states that a function f(x) is continuous at a point c if the limit of f(x) as x approaches c does not exist

The limit definition of continuity at a point states that a function f(x) is continuous at a point c if the function is not defined at c

The limit definition of continuity at a point states that a function f(x) is continuous at a point c if the limit is not equal to the value of the function at c

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the limit of f(x) = 3x - 2 as x approaches 4.

12

5

10

2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Determine the value of k that makes the function f(x) = 2x^2 + kx + 3 continuous at x = 2.

4

6

1

10

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Evaluate the limit lim(x->3) (x^2 - 9) / (x - 3).

3

9

6

0

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Explain the concept of one-sided limits and how they relate to continuity.

One-sided limits are used to determine the behavior of a function as it approaches a specific point from one direction. They relate to continuity by helping to identify if a function is continuous at a specific point.

One-sided limits are only applicable to linear functions and do not have any relation to continuity.

One-sided limits are used to determine the behavior of a function as it approaches a specific point from both directions. They relate to continuity by helping to identify if a function is discontinuous at a specific point.

One-sided limits are used to determine the behavior of a function as it moves away from a specific point. They relate to continuity by helping to identify if a function is undefined at a specific point.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the limit lim(x->0) (sinx / x).

1

0

2

sin(0)

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