Waste less time on Facebook — follow Brilliant.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Calculus
Taylor Series
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
Determine the Taylor series for the function
\[f(x)=\int _0 ^1 \dfrac{\sin x}{x}dx ~\text{ centered at }~ x=0.\]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
Evaluate \[\frac{\pi^2}{2!}-\frac{\pi^4}{4!}+\frac{\pi^6}{6!}-\frac{\pi^8}{8!}+\cdots.\]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
Determine the Taylor series for the function
\[f(x)=\sin x\cos x ~\text{ centered at }~ x=0.\]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
Evaluate
\[ \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \cdot 2^n }. \]
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
If \(f(x)=e^{x^2}\), what is \(f^{(2016)}(0)\) ?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff