What is the limit as x approaches infinity of (4^x+3)/(4^{x+1)} ?

The limit as x approaches infinity of (4^x+3)/(4^{x+1)} is 1/4

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limit as x approaches infinity of (4^x+3)/(4^{x+1)}

x \to \infty lim (\frac{4 ^{x} + 3}{4 ^{x + 1}})

\frac{1}{4}

Decimal

0.25

Solution steps

x \to \infty lim (\frac{4 ^{x} + 3}{4 ^{x + 1}})

Divide by

4^{x + 1} : \frac{1}{4} + \frac{3}{4 ^{x + 1}}

= x \to \infty lim (\frac{1}{4} + \frac{3}{4 ^{x + 1}})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (\frac{1}{4}) + x \to \infty lim (\frac{3}{4 ^{x + 1}})

x \to \infty lim (\frac{1}{4}) = \frac{1}{4}

x \to \infty lim (\frac{3}{4 ^{x + 1}}) = 0

= \frac{1}{4} + 0

Simplify

= \frac{1}{4}

f (x) = - \frac{2}{x}

\int (csc (x)) d x

\frac{d}{d x} (arctan (- 5 x + 1))

f (x) = 3 x^{2} + 5 x - 6

f (x) = arcsin (\frac{x}{3})

What is the limit as x approaches infinity of (4^x+3)/(4^{x+1)} ?
The limit as x approaches infinity of (4^x+3)/(4^{x+1)} is 1/4