What is the limit as x approaches 0 of ((19)/(x+20)-19/20)/x ?

The limit as x approaches 0 of ((19)/(x+20)-19/20)/x is -19/400

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limit as x approaches 0 of ((19)/(x+20)-19/20)/x

x \to 0 lim (\frac{\frac{19}{x + 20} - \frac{19}{20}}{x})

- \frac{19}{400}

Decimal

- 0.0475

Solution steps

x \to 0 lim (\frac{\frac{19}{x + 20} - \frac{19}{20}}{x})

Simplify

\frac{\frac{19}{x + 20} - \frac{19}{20}}{x} : - \frac{19}{20 ( x + 20 )}

= x \to 0 lim (- \frac{19}{20 ( x + 20 )})

Plug in the value

x = 0

= - \frac{19}{20 ( 0 + 20 )}

Simplify

= - \frac{19}{400}

x \to 1 + lim (\frac{3 x + 1}{x - 2})

x \to 3 lim (\frac{x ^{2} - 8}{x + 2})

x \to 1 lim (e^{- x^{2}})

x \to 1 + lim (- x)

x \to \frac{π}{2} lim (\frac{cos ^{2} ( x )}{( sin ( \frac{1}{2} ) x - cos ( \frac{1}{2} ) x ) ^{2}})

What is the limit as x approaches 0 of ((19)/(x+20)-19/20)/x ?
The limit as x approaches 0 of ((19)/(x+20)-19/20)/x is -19/400