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x→πlim​ sin x1+cos x​= ...

Pertanyaan

limit as x rightwards arrow straight pi of space fraction numerator 1 plus cos space x over denominator sin space x end fraction equals space...      

  1. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 2 end cell end table 

  2.  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 1 end cell end table 

  3. table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table  

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 0 comma 25 end cell end table  

  5.  table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 0 comma 5 end cell end table 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Seperti dalam limit fungsi aljabar, di dalam limit fungsi trigonometri, ada limit yang dapat ditentukan nilainya dengan mensubstitusi langsung nilai yang didekati, dan ada yang menghasilkan bentuk tak tentu apabila nilai yang didekati disubstitusi langsung.

Dengan mengubah bentuk fungsi, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi of space fraction numerator 1 plus cos space x over denominator sin space x end fraction end cell equals cell limit as x rightwards arrow straight pi of space fraction numerator 1 plus cos space x over denominator sin space x end fraction cross times fraction numerator 1 minus cos space x over denominator 1 minus cos space x end fraction end cell row blank equals cell limit as x rightwards arrow straight pi of space fraction numerator 1 minus cos squared space x over denominator sin space x open parentheses 1 minus cos space x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow straight pi of space fraction numerator sin squared space x over denominator sin space x open parentheses 1 minus cos space x close parentheses end fraction end cell row blank equals cell limit as x rightwards arrow straight pi of space fraction numerator sin space x over denominator 1 minus cos space x end fraction end cell row blank equals cell fraction numerator sin space 180 over denominator 1 minus cos space 180 end fraction end cell row blank equals 0 end table      

Maka, table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow straight pi of space fraction numerator 1 plus cos space x over denominator sin space x end fraction end cell equals 0 end table

Oleh karena itu, jawaban yang benar adalah C.

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