/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 Is \(x^{12}\) an even or odd fun... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 3

Is \(x^{12}\) an even or odd function? Is \(\sin x^{2}\) an even or odd function?

Short Answer

Expert verified
Question: Determine whether the functions \(x^{12}\) and \(\sin x^{2}\) are even or odd. Answer: The function \(x^{12}\) is an even function, and the function \(\sin x^{2}\) is also an even function.

Step by step solution

01

Analyze the function \(x^{12}\) for evenness and oddness

First, we will determine whether the function \(x^{12}\) is even or odd by plugging in \(-x\) for \(x\) and see which condition it satisfies: \(f(-x) = (-x)^{12} \) As \((-x)^{12}=x^{12}\), the function \(f(x)=x^{12}\) satisfies the condition for even functions: \(f(-x) = f(x)\) So, \(x^{12}\) is an even function.
02

Analyze the function \(\sin x^{2}\) for evenness and oddness

Next, we will determine whether the function \(\sin x^{2}\) is even or odd by plugging in \(-x\) for \(x\) and see which condition it satisfies: \(f(-x) = \sin (-x)^{2} = \sin x^{2}\) As \(\sin (-x)^{2} = \sin x^{2}\), the function \(f(x) = \sin x^{2}\) satisfies the condition for even functions: \(f(-x) = f(x)\) So, \(\sin x^{2}\) is an even function. In conclusion, the function \(x^{12}\) is an even function, and the function \(\sin x^{2}\) is also an even function.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Additional integrals Use a change of variables to evaluate the following integrals. $$\int\left(\sin ^{5} x+3 \sin ^{3} x-\sin x\right) \cos x d x$$

Assume that the linear function \(f(x)=m x+c\) is positive on the interval \([a, b] .\) Prove that the midpoint Riemann sum with any value of \(n\) gives the exact area of the region between the graph of \(f\) and the \(x\) -axis on \([a, b]\).

Consider the function \(f\) and the points \(a, b,\) and \(c\) a. Find the area function \(A(x)=\int_{a}^{x} f(t) d t\) using the Fundamental Theorem. b. Graph \(f\) and \(A\) c. Evaluate \(A(b)\) and \(A(c)\) and interpret the results using the graphs of part \((b)\) $$f(x)=\cos \pi x ; a=0, b=\frac{1}{2}, c=1$$

Evaluate the following definite integrals using the Fundamental Theorem of Calculus. $$\int_{0}^{\pi / 3} \sec x \tan x d x$$

Consider the graph of the cubic \(y=x(x-a)(x-b),\) where \(0
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.