QQuestionMathematics
QuestionMathematics
Find the nth Maclaurin polynomial for the function.
Function: f(2$) = sin(2$)
Degree: n = 3
P^3(x )= ___
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:I'll solve this step-by-step using the Maclaurin series for sin(x).
Step 2:: Recall the Maclaurin series for sin(x)
The Maclaurin series for $$\sin(x)$$ is:
\sin(x) = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + \cdots
Step 3:: Identify the terms for the 3rd degree Maclaurin polynomial
For a 3rd degree (n = 3) polynomial, we'll include terms up to $$x^{3}$$:
P_{3}(x) = x - \frac{x^{3}}{3!}
Step 4:: Simplify the factorial term
\frac{x^{3}}{3!} = \frac{x^{3}}{6}
Step 5:: Write the final 3rd degree Maclaurin polynomial
P_{3}(x) = x - \frac{x^{3}}{6}
Final Answer
P_{3}(x) = x - \frac{x^{3}}{6}
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students