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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{d y}{d x} + cos (x) = (y + sin (x))^{2}

f (x) = sin (2 x) cos (2 x)

\frac{4 x}{x + 1}

\int e^{- 5 x} sin (4 x) d x

\frac{d y}{d x} = \frac{x}{y}, y (0) = - 4

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