What is the limit as x approaches 0 of ((4^{2x}-1))/((4^x-1)) ?

The limit as x approaches 0 of ((4^{2x}-1))/((4^x-1)) is 2

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limit as x approaches 0 of ((4^{2x}-1))/((4^x-1))

x \to 0 lim (\frac{( 4 ^{2 x} - 1 )}{( 4 ^{x} - 1 )})

2

Solution steps

x \to 0 lim (\frac{4 ^{2 x} - 1}{4 ^{x} - 1})

Simplify

\frac{4 ^{2 x} - 1}{4 ^{x} - 1} : 4^{x} + 1

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

Plug in the value

x = 0

= 4^{0} + 1

Simplify

= 2

z \to 2 lim (\frac{z ^{2} + 3}{i z})

ln (1 + 7 x)

\frac{d ^{2}}{d x ^{2}} (4 x + 15)

\frac{\partial}{\partial x} (xx + yy)

\int_{0}^{π} x \cdot cos (x) d x

What is the limit as x approaches 0 of ((4^{2x}-1))/((4^x-1)) ?
The limit as x approaches 0 of ((4^{2x}-1))/((4^x-1)) is 2