Understanding Continuity in Trigonometric Functions

Understanding Continuity in Trigonometric Functions

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Hard

CCSS
HSF.BF.B.5, HSF.TF.A.4, 6.EE.B.8

+1

Standards-aligned

Created by

Ethan Morris

FREE Resource

Standards-aligned

CCSS.HSF.BF.B.5
,
CCSS.HSF.TF.A.4
,
CCSS.6.EE.B.8
CCSS.HSF-IF.C.7D
,
The video tutorial explains how to determine the interval of continuity for a function involving tangent and sine, divided by a natural logarithm. It reviews the properties of natural logarithms, analyzes the tangent function, and solves for restrictions on x. The interval of continuity is formed by considering these restrictions and is expressed using interval notation.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the interval over which we need to determine the continuity of the function?

From 0 to π

From 0 to 2π

From -2π to 2π

From -π to π

Tags

CCSS.HSF.BF.B.5

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why can't the natural log of 2x divided by π equal zero?

Because it would make the function continuous

Because it would make the function positive

Because it would make the function undefined

Because it would make the function negative

Tags

CCSS.HSF.BF.B.5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What must be true about the expression 2x divided by π for the function to be continuous?

It must be equal to one

It must be greater than zero

It must be equal to zero

It must be less than zero

Tags

CCSS.HSF.TF.A.4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the range of possible outputs for sine x?

From -1 to 1

From 0 to 2

From -2 to 2

From 0 to 1

Tags

CCSS.HSF.TF.A.4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the tangent function continuous over the interval of sine x?

Because sine x is always positive

Because sine x is always negative

Because sine x is equal to zero

Because sine x is within the range -1 to 1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What value of x must be excluded to maintain continuity?

x = 0

x = 2π

x = π/2

x = π

Tags

CCSS.6.EE.B.8

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of solving the inequality 2x divided by π > 0?

x = π

x = 0

x < 0

x > 0

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