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domäne 6ln(x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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f(x)=log₂(2x)

Solution

Domain: x>0

Range: −∞ <f(x)<∞

X−Schnittpunkte: (12 , 0)

Asymptotes: Vertikal x=0

Extreme Points: Keine

Interval Notation

Domain: (0, ∞ )

Range: (−∞ , ∞ )

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Solution steps

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∫ e^xcos(nx)dx

Wende die partielle Integration an: e^x1n sin(nx)−∫ e^x1n sin(nx)dx

=e^x1n sin(nx)−∫ e^x1n sin(nx)dx

Entferne die Konstante: ∫a·f(x)dx=a·∫f(x)dx

=e^x1n sin(nx)−1n · ∫ e^xsin(nx)dx

Wende die partielle Integration an: −e^x1n cos(nx)−∫ −e^x1n cos(nx)dx

=e^x1n sin(nx)−1n (−e^x1n cos(nx)−∫ −e^x1n cos(nx)dx)

Entferne die Konstante: ∫a·f(x)dx=a·∫f(x)dx

=e^x1n sin(nx)−1n (−e^x1n cos(nx)−(−1n · ∫ e^xcos(nx)dx))

Deshalb

∫ e^xcos(nx)dx=e^x1n sin(nx)−1n (−e^x1n cos(nx)−(−1n · ∫ e^xcos(nx)dx))

Isoliere ∫ e^xcos(nx)dx

=ne^xsin(nx)n²+1 +e^xcos(nx)n²+1

Füge eine Konstante zur Lösung hinzu

=ne^xsin(nx)n²+1 +e^xcos(nx)n²+1 +C

Solve instead

ddx (log₂(2x))

invers log₂(2x)

geradzahligkeit log₂(2x)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

domäne 6ln(x)

Solution

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