Question

qual o lim da equação? ​

Answer 1

Resposta:

$\red{ \frac{ \sqrt[ 3]{975} }{5} }$

Explicação passo-a-passo:

$\lim_{x \to \ - 2} \sqrt[3]{ \frac{ {3x}^{3} { - 5x}^{2} - x + 3 }{4x + 3} }$

$\sqrt[3]{ {\lim_{x \to -2} }^{( \frac{ {3x}^{3} { - 5x}^{2} - x + 3}{4x + 3}) } }$

$\sqrt[3]{ \frac{ {\lim_{x \to -2} }^{( {3x}^{3} { - 5x}^{2} - x + 3)} }{ {\lim_{x \to -2} }^{(4x + 3)} } }$

$\sqrt[3]{ \frac{ {\lim_{x \to -2} }^{( {3x}^{3} { - 5x}^{2} - x)} + {\lim_{x \to -2} }^{(3)} }{ {\lim_{x \to -2} }^{(4x) } + {\lim_{x \to -2} }^{(3)} } }$

$\sqrt[3]{ \frac{ {\lim_{x \to -2} }^{( {3x}^{3} { - 5x}^{2} ) - {\lim_{x \to -2} }^{(x) + 3} } }{ {4 \times \lim_{x \to -2} }^{(x)} + {\lim_{x \to -2} }^{(3)} } }$

$\sqrt[3]{ \frac{ {\lim_{x \to -2} }^{( {3x}^{3} { - 5x}^{2} ) - {\lim_{x \to -2} }^{(x) + 3} } }{4 \times {\lim_{x \to -2} }^{(x) + 3} } }$

$\sqrt[ 3]{ \frac{ {\lim_{x \to -2} }^{ {(3x}^{3}) - {\lim_{x \to -2} }^{ {(5x}^{2}) - ( - 2) + 3 } } }{4 \times ( - 2) + 3} }$

$\sqrt[3]{ \frac{ {3 \times \lim_{x \to -2} }^{ {(x}^{3}) } - 5 \times \: \: {\lim_{x \to -2} }^{ {(x}^{2}) } - ( - 2) + 3}{4 \times ( - 2) + 3} }$

$\sqrt[3]{ \frac{3 \times ( {\lim_{x \to -2} }^{ {(x)} } )^{3} - 5 \times ( {\lim_{x \to -2} }^{(x)})^{2} - 2( - 2) + 3 }{4 \times ( - 2) + 3} }$

$\sqrt[3]{ \frac{3 \times {( - 2)}^{3} - 5 \times {( - 2)}^{2} - ( - 2) + 3 }{4 \times ( - 2) + 3} }$

$\sqrt[3]{ \frac{3 \times ( { - 2}^{3}) - 5 \times {2}^{2} + 2 + 3 }{ - 8 + 3} }$

$\sqrt[3]{ \frac{ - 3 \times 8 - 5 \times 4 + 2 + 3}{ - 8 + 3} }$

$\sqrt[3]{ \frac{ - 3 \times 8 - 5 \times 4 + 2 + 3}{ - 5} }$

$\sqrt[3]{ \frac{ - 24 - 20 + 2 + 3}{ - 5} }$

$\sqrt[3]{ \frac{ - 39}{ - 5} }$

$\sqrt[3]{ \frac{39}{5} }$

$\frac{ \sqrt[3]{39} }{ \sqrt[3]{5} }$

$\frac{ \sqrt[3]{39 \times {5}^{2} } }{5}$

$\sqrt[3]{ \frac{39 \times 25}{5} }$

$\red{ \frac{ \sqrt[ 3]{975} }{5} }$

ATT:ARMANDO