What is the limit as x approaches 3 of ((x^3-5x+6)^{40})/((x^4-10x^2+9)^{20)} ?

The limit as x approaches 3 of ((x^3-5x+6)^{40})/((x^4-10x^2+9)^{20)} is infinity

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limit as x approaches 3 of ((x^3-5x+6)^{40})/((x^4-10x^2+9)^{20)}

x \to 3 lim (\frac{( x ^{3} - 5 x + 6 ) ^{40}}{( x ^{4} - 10 x ^{2} + 9 ) ^{20}})

\infty

Solution steps

x \to 3 lim (\frac{( x ^{3} - 5 x + 6 ) ^{40}}{( x ^{4} - 10 x ^{2} + 9 ) ^{20}})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 3 - lim (\frac{( x ^{3} - 5 x + 6 ) ^{40}}{( x ^{4} - 10 x ^{2} + 9 ) ^{20}}) = \infty

x \to 3 + lim (\frac{( x ^{3} - 5 x + 6 ) ^{40}}{( x ^{4} - 10 x ^{2} + 9 ) ^{20}}) = \infty

= \infty

What is the limit as x approaches 3 of ((x^3-5x+6)^{40})/((x^4-10x^2+9)^{20)} ?
The limit as x approaches 3 of ((x^3-5x+6)^{40})/((x^4-10x^2+9)^{20)} is infinity