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

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

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

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Plug in the value

x = 2

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

Simplify

= \frac{1}{3}

x \to 2 lim (- x + 1)

x \to 4 lim (\frac{x ^{2} - 3 x - 4}{2 x + 1})

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

x \to 5 - lim (\frac{( 1 )}{x - 5})

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

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