What is the limit as x approaches infinity of (+x-2^{+x})/(3^x-5) ?

The limit as x approaches infinity of (+x-2^{+x})/(3^x-5) is 0

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limit as x approaches infinity of (+x-2^{+x})/(3^x-5)

x \to \infty lim (\frac{+ x - 2 ^{+ x}}{3 ^{x} - 5})

0

Solution steps

x \to \infty lim (\frac{x - 2 ^{x}}{3 ^{x} - 5})

Divide by

3^{x} : \frac{\frac{x}{3 ^{x}} - ( \frac{2}{3} ) ^{x}}{1 - \frac{5}{3 ^{x}}}

= x \to \infty lim (\frac{\frac{x}{3 ^{x}} - ( \frac{2}{3} ) ^{x}}{1 - \frac{5}{3 ^{x}}})

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} ( \frac{x}{3 ^{x}} - ( \frac{2}{3} ) ^{x} )}{lim _{x \to \infty} ( 1 - \frac{5}{3 ^{x}} )}

x \to \infty lim (\frac{x}{3 ^{x}} - (\frac{2}{3})^{x}) = 0

x \to \infty lim (1 - \frac{5}{3 ^{x}}) = 1

= \frac{0}{1}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

\int 5 \frac{cos ( x ) + sin ( x )}{sin ( 2 x )} d x

f (x) = \frac{x}{x ^{2} + 81}

\int_{0}^{1} (1 - x^{3}) d x

\frac{d}{d x} ((tan (2 x))^{3})

y^{^{'}} = 1 - y^{2}

What is the limit as x approaches infinity of (+x-2^{+x})/(3^x-5) ?
The limit as x approaches infinity of (+x-2^{+x})/(3^x-5) is 0