Calculus II Sequence Problems

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App

Questions and Answers

Match the following functions with their corresponding solutions:

f(x) = (1+x)^2 = x = 0 = 1 = 1 + f(x) = 2x = n = 0 = +1 => f(x) = tan(x) = x = 0 = f(x) = 0 + f(x) = x^2 tan(x) = 1 3 taix-t taix=M( 2n n

Match the following functions with their corresponding expressions:

f(x) = sin(x) = f(x) = (y" - x) / (x - y) f(x) = e^x = f(x) = x^n / n! f(x) = x^2 = f(x) = x^2 / (2n + 1) f(x) = tan(x) = f(x) = x / (x^2 + 1)

Match the following functions with their corresponding derivatives:

f(x) = x^2 = f'(x) = 2x f(x) = e^x = f'(x) = e^x f(x) = tan(x) = f'(x) = sec^2(x) f(x) = sin(x) = f'(x) = cos(x)

Match the following functions with their corresponding integrals:

<p>f(x) = x^2 = ∫f(x)dx = x^3 / 3 + C f(x) = e^x = ∫f(x)dx = e^x + C f(x) = tan(x) = ∫f(x)dx = -ln|cos(x)| + C f(x) = sin(x) = ∫f(x)dx = -cos(x) + C</p> Signup and view all the answers

Match the following functions with their corresponding power series expansions:

<p>f(x) = e^x = ∑(x^n / n!) f(x) = sin(x) = ∑((-1)^n * x^(2n+1) / (2n+1)!) f(x) = tan(x) = ∑(x^(2n+1) / (2n+1)!) f(x) = x^2 = ∑(x^(2n) / (2n)!)</p> Signup and view all the answers

Match the following functions with their corresponding Taylor series expansions:

<p>f(x) = e^x = ∑(x^n / n!) f(x) = sin(x) = ∑(x^(2n+1) / (2n+1)!) f(x) = tan(x) = ∑(x^(2n+1) / (2n+1)!) f(x) = x^2 = ∑(x^(2n) / (2n)!)</p> Signup and view all the answers

Match the following functions with their corresponding radius of convergence:

<p>f(x) = e^x = R = ∞ f(x) = sin(x) = R = ∞ f(x) = tan(x) = R = π/2 f(x) = x^2 = R = ∞</p> Signup and view all the answers

Match the following functions with their corresponding series expansions:

<p>f(x) = e^x = 1 + x + x^2 / 2! +... f(x) = sin(x) = x - x^3 / 3! + x^5 / 5! -... f(x) = tan(x) = x + x^3 / 3 + 2x^5 / 15 +... f(x) = x^2 = x^2 + x^4 / 2 + x^6 / 6 +...</p> Signup and view all the answers

Match the following functions with their corresponding general terms:

<p>f(x) = e^x = x^n / n! f(x) = sin(x) = (-1)^n * x^(2n+1) / (2n+1)! f(x) = tan(x) = x^(2n+1) / (2n+1)! f(x) = x^2 = x^(2n) / (2n)!</p> Signup and view all the answers

Match the following functions with their corresponding intervals of convergence:

<p>f(x) = e^x = (-∞, ∞) f(x) = sin(x) = (-∞, ∞) f(x) = tan(x) = (-π/2, π/2) f(x) = x^2 = (-∞, ∞)</p> Signup and view all the answers

Flashcards are hidden until you start studying

More Like This

Sequence Modeling Quiz
10 questions

Sequence Modeling Quiz

WellBalancedSpessartine avatar
WellBalancedSpessartine
Recurrence Relation Sequence Problem
111 questions
Vraagstukken Oplossen & Fibonacci
39 questions
Use Quizgecko on...
Browser
Browser