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Pertanyaan

Find the value of the limit. t → 0 lim ​ 2 − 4 − t ​ t ​

Find the value of the limit.

 

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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Pembahasan

Dengan mengalikan akar sekawan, diperoleh: Sehingga,

Dengan mengalikan akar sekawan, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as t rightwards arrow 0 of fraction numerator t over denominator 2 minus square root of 4 minus t end root end fraction end cell equals cell limit as t rightwards arrow 0 of fraction numerator t over denominator 2 minus square root of 4 minus t end root end fraction cross times fraction numerator 2 plus square root of 4 minus t end root over denominator 2 plus square root of 4 minus t end root end fraction end cell row blank equals cell limit as t rightwards arrow 0 of fraction numerator t cross times open parentheses 2 plus square root of 4 minus t end root close parentheses over denominator 4 minus open parentheses 4 minus t close parentheses end fraction end cell row blank equals cell limit as t rightwards arrow 0 of fraction numerator t cross times open parentheses 2 plus square root of 4 minus t end root close parentheses over denominator t end fraction end cell row blank equals cell limit as t rightwards arrow 0 of 2 plus square root of 4 minus t end root end cell row blank equals cell limit as t rightwards arrow 0 of 2 plus square root of 4 minus 0 end root end cell row blank equals cell limit as t rightwards arrow 0 of 2 plus 2 end cell row blank equals 4 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell limit as t rightwards arrow 0 of fraction numerator t over denominator 2 minus square root of 4 minus t end root end fraction end cell equals 4 end table

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