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

The limit as x approaches 0 of 1/((x-1)^4+2) is 1/3

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Plug in the value

x = 0

= \frac{1}{( 0 - 1 ) ^{4} + 2}

(0 - 1)^{4} + 2 = 3

= \frac{1}{3}

x \to - \infty lim (x + e^{x})

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

x \to - 2 lim (2 e^{x + 2} - 3)

x \to 0 + lim (\frac{4}{x} - ln (x))

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

What is the limit as x approaches 0 of 1/((x-1)^4+2) ?
The limit as x approaches 0 of 1/((x-1)^4+2) is 1/3