What is the limit as x approaches-infinity of ((3^{6x}+6))/((3^{2x)+4)} ?

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

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limit as x approaches-infinity of ((3^{6x}+6))/((3^{2x)+4)}

x \to - \infty lim (\frac{( 3 ^{6 x} + 6 )}{( 3 ^{2 x} + 4 )})

\frac{3}{2}

Decimal

1.5

Solution steps

x \to - \infty lim (\frac{3 ^{6 x} + 6}{3 ^{2 x} + 4})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to - \infty} ( 3 ^{6 x} + 6 )}{lim _{x \to - \infty} ( 3 ^{2 x} + 4 )}

x \to - \infty lim (3^{6 x} + 6) = 6

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

= \frac{6}{4}

Cancel the common factor:

2

= \frac{3}{2}

\frac{d}{d x} (lo g_{e} (x^{2}))

t \to \infty lim (t)

(\frac{2 + 5 z}{5 z}) (15 - 2 z)

y = 3 sec (x), at x = \frac{π}{6}

\int_{0}^{3} 9 - x^{2} d x

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