Pertanyaan

x → ∞ lim ( ( 2 x + 1 ) − 4 x 2 + 3 x + 9 ) = ....

$x \to \infty lim ((2 x + 1) - 4 x^{2} + 3 x + 9) = ....$

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Pembahasan

Pada limit tak hingga, misal maka, nilai limitnya adalah

Pada limit tak hingga, misal

$limit as x rightwards arrow infinity of square root of a x squared plus b x plus c end root minus square root of p x squared plus q x plus r end root equals L L equals fraction numerator b minus q over denominator 2 square root of a end fraction comma space j i k a space a equals p$

maka, nilai limitnya adalah

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell limit as x rightwards arrow infinity of square root of open parentheses 2 x plus 1 close parentheses squared end root minus square root of 4 x squared plus 3 x plus 9 end root end cell row blank equals cell limit as x rightwards arrow infinity of square root of 4 x squared plus 4 x plus 1 end root minus square root of 4 x squared plus 3 x plus 9 end root end cell row blank equals cell fraction numerator b minus q over denominator 2 square root of a end fraction end cell row blank equals cell fraction numerator 4 minus 3 over denominator 2 square root of 4 end fraction end cell row blank equals cell 1 fourth end cell end table end style$