What is the limit as x approaches y of (x^n-y^n)/(x-y) ?

The limit as x approaches y of (x^n-y^n)/(x-y) is ny^{n-1}

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limit as x approaches y of (x^n-y^n)/(x-y)

x \to y lim (\frac{x ^{n} - y ^{n}}{x - y})

n y^{n - 1}

Solution steps

x \to y lim (\frac{x ^{n} - y ^{n}}{x - y})

Apply L'Hopital's Rule

: x \to y lim (\frac{n x ^{n - 1}}{1})

= x \to y lim (\frac{n x ^{n - 1}}{1})

Plug in the value

x = y

= \frac{n y ^{n - 1}}{1}

Simplify

= n y^{n - 1}

e^{5 x}, e^{7 x}, 1

\int 3 x \cdot e^{- 2 x} d x

\int \frac{x ^{2}}{x ^{2} + 16} d x

e^{x} \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

f (x) = cos (π x)

What is the limit as x approaches y of (x^n-y^n)/(x-y) ?
The limit as x approaches y of (x^n-y^n)/(x-y) is ny^{n-1}