limit as x approaches infinity of csc(1/x)-cot(1/x)

Lösung

x \to \infty lim (csc (\frac{1}{x}) - cot (\frac{1}{x}))

0

Schritte zur Lösung

x \to \infty lim (csc (\frac{1}{x}) - cot (\frac{1}{x}))

Drücke mit sin, cos aus

= x \to \infty lim (\frac{1 - cos ( \frac{1}{x} )}{sin ( \frac{1}{x} )})

Wende das L'Hopital Theorem an

= x \to \infty lim \frac{- \frac{s i n ( \frac{1}{x} )}{x ^{2}}}{- \frac{c o s ( \frac{1}{x} )}{x ^{2}}}

Vereinfache

\frac{- \frac{s i n ( \frac{1}{x} )}{x ^{2}}}{- \frac{c o s ( \frac{1}{x} )}{x ^{2}}} : tan (\frac{1}{x})

= x \to \infty lim (tan (\frac{1}{x}))

Wende die Kettenregel für Grenzen an:

0

= 0

y^{^{''}} - 14 y^{^{'}} + 74 y = 0

\int 5 x ln (2 x) d x

\frac{d}{d x} (2^{\frac{x}{2}})

t an g e n t - \frac{1}{x}, at x = 3

\frac{d}{d x} (\frac{1}{2 x + 4})