Comprehensive Calculus and Mathematical Analysis Flashcards

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Comprehensive Calculus and Mathematical Analysis

Essential topics in calculus and analysis, including limits, differentiation rules, integration techniques, sequences, and fundamental theorems.

What is the limit of $\frac{s i n x}{x}$ as $x$ approaches $0$

$1$

What is the derivative of a constant $c$

$0$

What is the derivative of $x^{n}$

$n x^{n - 1}$

What is the derivative of $e^{x}$

$e^{x}$

What is the derivative of $ln (x)$

$\frac{1}{x}$

What is the derivative of $sin x$

$cos x$

What is the derivative of $cos x$

$- sin x$

What is the derivative of $tan x$

$sec^{2} x$

What is the derivative of $sec x$

$sec x tan x$

What rule is used for the derivative of $f (g (x))$

The chain rule, $f^{'} (g (x)) g^{'} (x)$

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