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x → ∞ lim ​ x + 2 ​ − x + 4 ​ = ....

 ....

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

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0.

 limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root equals 0.

Pembahasan

Limit Tak Hingga Karena dalam bentuk akar, maka kita kalian bilangan sekawan Jadi, 0.

Limit Tak Hingga

Karena dalam bentuk akar, maka kita kalian bilangan sekawan

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root cross times fraction numerator square root of x plus 2 end root plus square root of x plus 4 end root over denominator square root of x plus 2 end root plus square root of x plus 4 end root end fraction end cell row blank equals cell stack l i m with x rightwards arrow infinity below fraction numerator open parentheses x plus 2 close parentheses minus open parentheses x plus 4 close parentheses over denominator square root of x plus 2 end root plus square root of x plus 4 end root end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator negative 2 over denominator square root of x plus 2 end root plus square root of x plus 4 end root end fraction cross times fraction numerator square root of x over denominator square root of x end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style fraction numerator negative 2 over denominator square root of x end fraction end style over denominator square root of begin display style x over x end style plus begin display style 2 over x end style end root plus square root of begin display style x over x end style plus begin display style 4 over x end style end root end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 2 over denominator infinity end fraction end style over denominator square root of 1 plus begin display style 2 over infinity end style end root plus square root of 1 plus begin display style 4 over infinity end style end root end fraction end cell row blank equals cell fraction numerator 0 over denominator square root of 1 plus square root of 1 end fraction end cell row blank equals cell 0 over 2 end cell row blank equals 0 end table 

Jadi, limit as x rightwards arrow infinity of square root of x plus 2 end root minus square root of x plus 4 end root equals 0.

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