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Taylor Series

Concept Quizzes

Local Linear Approximation
Taylor Series
Taylor Series Approximation
Taylor Series Manipulation
Taylor Series - Interval and Radius of Convergence
Taylor Series - Error Bounds
Taylor Series - Problem Solving

Challenge Quizzes

Taylor Series: Level 3 Challenges
Taylor Series: Level 4 Challenges
Taylor Series: Level 5 Challenges

Taylor Series Manipulation

Determine the Taylor series for the function

\[f(x)=\sinh x ~\text{ centered at }~ x=0.\]

\[ \sum_{n = 0}^{\infty}\frac{x^{2n-1}}{(2n-1)!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{n+2}}{(2n+1)!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{2n+1}}{(2n+1)!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{2n-1}}{(2n-1)}\]

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by Brilliant Staff

Determine the Taylor series for the function

\[f(x)=\cosh x ~\text{ centered at }~ x=0.\]

\[ \sum_{n = 0}^{\infty}\frac{x^{n+2}}{(2n+2)!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{2n-1}}{(2n-1)!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{2n}}{(2n)!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{2n+1}}{(2n+1)}\]

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by Brilliant Staff

Determine the Taylor series for the function

\[f(x)=e^{x^2} ~\text{ centered at }~ x=0.\]

\[ \sum_{n = 0}^{\infty}\frac{2x^{n}}{n!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{n^2}}{n!}\] \[ \sum_{n = 0}^{\infty}\frac{(2x)^{n}}{n!}\] \[ \sum_{n = 0}^{\infty}\frac{x^{2n}}{n!}\]

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by Brilliant Staff

Determine the Taylor series for the function

\[f(x)=\frac{1}{(1 - x)^2} ~\text{ centered at }~ x=0 ~\text{ for }~ \left |x \right |<1.\]

\[\sum_{n = 0}^{\infty}nx^n \] \[\sum_{n = 0}^{\infty}(n+1)x^{n+1} \] \[\sum_{n = 0}^{\infty}nx^{n+1} \] \[\sum_{n = 0}^{\infty}(n+1)x^n \]

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by Brilliant Staff

Determine the Taylor series for the function

\[f(x)=\sin{x^2} ~\text{ centered at }~ x=0.\]

\[ \sum_{n = 0}^{\infty}\frac{(-1)^n (2x)^{2n+1}}{(2n+1)!} \] \[ \sum_{n = 0}^{\infty}\frac{(-1)^n x^{4n+2}}{(2n+1)!} \] \[ \sum_{n = 0}^{\infty}\frac{(-1)^{2n} x^{4n+2}}{(2n+1)!} \] \[ \sum_{n = 0}^{\infty}\frac{(-1)^n x^{4n+2}}{(4n+2)!} \]

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by Brilliant Staff

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