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

The limit as x approaches i of (x^4-1)/(x-i) is -4i

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

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

- 4 i

Solution steps

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

Rationalize denominator

\frac{x ^{4} - 1}{x - i} : (x^{3} - x) + i (- 1 + x^{2})

= x \to i lim (x^{3} - x + i (- 1 + x^{2}))

Plug in the value

x = i

= i^{3} - i + i (- 1 + i^{2})

Simplify

i^{3} - i + i (- 1 + i^{2}) : - 4 i

= - 4 i

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