Waste less time on Facebook — follow Brilliant.
Already have an account? Log in here.
Calculus Warmups
The concepts of limits, infinitesimal partitions, and continuously changing quantities paved the way to Calculus, the universal tool for modeling continuous systems from Physics to Economics. See more
Already have an account? Log in here.
by
Siddharth Goel
\[\large\sum _{ j=0 }^{ \infty }{ \sum _{ i=0 }^{ \infty }{ \frac { { 2 }^{ -(i+j) } }{ i+j+1 } } } = \ ?\]
Give your answer to 3 decimal places.
Already have an account? Log in here.
by
Aditya Kumar
\[ \large \lim _{xy\to 1}\left(\frac{\ln\:x}{\ln\:y}+\frac{\ln\:y}{\ln\:x}\right)= \ ? \]
Already have an account? Log in here.
by
Efren Medallo
\[ \large 2 \times \lim_{h\to0} \dfrac{\int_1^{1+h} x^x \, dx - \int_{1-h}^1 x^x \, dx }{h^2} =\, ? \]
Already have an account? Log in here.
by
Pi Han Goh
Some people claim that \( 0 ^ 0 = 1 \). What is
\[ \Large \lim_{ x \rightarrow 0^+ } x ^ { \frac{ 1}{\ln x} }?\]
Already have an account? Log in here.
by
Calvin Lin