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

The limit as x approaches 0+of (x+1)/(2^x-1) is infinity

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limit as x approaches 0+of (x+1)/(2^x-1)

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

\infty

Solution steps

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

\frac{x + 1}{2 ^{x} - 1} = (x + 1) \frac{1}{2 ^{x} - 1}

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

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

With the exception of indeterminate form

= x \to 0 + lim (x + 1) \cdot x \to 0 + lim (\frac{1}{2 ^{x} - 1})

x \to 0 + lim (x + 1) = 1

x \to 0 + lim (\frac{1}{2 ^{x} - 1}) = \infty

= 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 1 - lim (x^{2} - 10 x + 8)

x \to 2 - lim (x tan (x))

x \to - 3 - lim (\frac{( x ) + 1}{x})

x \to 0 lim (csc (2 x) tan (3 x))

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

What is the limit as x approaches 0+of (x+1)/(2^x-1) ?
The limit as x approaches 0+of (x+1)/(2^x-1) is infinity