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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.
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.
by
Aditya Kumar
\[ \large \lim _{xy\to 1}\left(\frac{\ln\:x}{\ln\:y}+\frac{\ln\:y}{\ln\:x}\right)= \ ? \]
by
Efren Medallo
\[ \large 2 \times \lim_{h\to0} \dfrac{\int_1^{1+h} x^x \, dx - \int_{1-h}^1 x^x \, dx }{h^2} =\, ? \]
by
Pi Han Goh
Some people claim that \( 0 ^ 0 = 1 \). What is
\[ \Large \lim_{ x \rightarrow 0^+ } x ^ { \frac{ 1}{\ln x} }?\]
by
Calvin Lin