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Dengan teorema L'Hospital hitunglah limit-limit fungsi berikut. x→0lim​ x22−2 cos 2x​

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Dengan teorema L'Hospital hitunglah limit-limit fungsi berikut.

begin mathsize 14px style limit as x rightwards arrow 0 of space fraction numerator 2 minus 2 space cos space 2 x over denominator x squared end fraction end style

N. Puspita

Master Teacher

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 begin mathsize 14px style limit as x rightwards arrow 0 of space fraction numerator 2 minus 2 space cos space 2 x over denominator x squared end fraction equals 4 end style

Pembahasan

Limit fungsi trigonometri: begin mathsize 14px style limit as x rightwards arrow 0 of space fraction numerator sin space a x over denominator a x end fraction equals 1 end style

Dengan teorema L'Hospital, nilai limit fungsi tersebut dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow 0 of space fraction numerator 2 minus 2 space cos space 2 x over denominator x squared end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator negative 2 space open parentheses negative 2 space sin space 2 x close parentheses over denominator 2 x end fraction end cell row blank equals cell limit as x rightwards arrow 0 of space fraction numerator 4 space sin space 2 x over denominator 2 x end fraction end cell row blank equals cell 4 times 1 end cell row blank equals 4 end table end style

Dengan demikian, begin mathsize 14px style limit as x rightwards arrow 0 of space fraction numerator 2 minus 2 space cos space 2 x over denominator x squared end fraction equals 4 end style

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