Pertanyaan

x → ∞ lim ( 4 x 2 + 5 x + 5 − 4 x 2 + x − 3 ) = ...

$x \to \infty lim (4 x^{2} + 5 x + 5 - 4 x^{2} + x - 3) = ...$

P. Anggrayni

Master Teacher

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Jawaban

dapat disimpulkan bahwa nilai .

dapat disimpulkan bahwa nilai limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x plus 5 end root minus square root of 4 x squared plus x minus 3 end root close parentheses equals 1

limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x plus 5 end root minus square root of 4 x squared plus x minus 3 end root close parentheses equals 1

Pembahasan

Ingat rumus umum untuk menyelesaikan limit seperti pada soal yaitu Perhatikan bahwa dari bentuk diperoleh Maka Jadi, dapat disimpulkan bahwa nilai .

Ingat rumus umum untuk menyelesaikan limit seperti pada soal yaitu

$limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of a x squared plus p x plus q end root equals fraction numerator b minus p over denominator 2 square root of a end fraction$

Perhatikan bahwa dari bentuk

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of left parenthesis square root of 4 x squared plus 5 x plus 5 end root minus square root of 4 x squared plus x minus 3 end root right parenthesis end cell row blank blank blank end table

diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 4 space space space p equals 4 end cell row b equals cell 5 space space space q equals 1 end cell row c equals cell 5 space space space r equals negative 3 end cell end table

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of left parenthesis square root of 4 x squared plus 5 x plus 5 end root minus square root of 4 x squared plus x minus 3 end root right parenthesis end cell equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 5 minus 1 over denominator 2 square root of 4 end fraction end cell row blank equals cell 4 over 4 end cell row blank equals 1 end table$

Jadi, dapat disimpulkan bahwa nilai limit as x rightwards arrow infinity of open parentheses square root of 4 x squared plus 5 x plus 5 end root minus square root of 4 x squared plus x minus 3 end root close parentheses equals 1 .

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