What is the limit as x approaches pi of ((x^{10}-pi^{10}))/(x-pi) ?

The limit as x approaches pi of ((x^{10}-pi^{10}))/(x-pi) is 10pi^9

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limit as x approaches pi of ((x^{10}-pi^{10}))/(x-pi)

x \to π lim (\frac{( x ^{10} - π ^{10} )}{x - π})

10 π^{9}

Decimal

298090.99333 \dots

Solution steps

x \to π lim (\frac{x ^{10} - π ^{10}}{x - π})

Simplify

\frac{x ^{10} - π ^{10}}{x - π} : (x + π) (x^{4} - π x^{3} + π^{2} x^{2} - π^{3} x + π^{4}) (x^{4} + π x^{3} + π^{2} x^{2} + π^{3} x + π^{4})

= x \to π lim ((x + π) (x^{4} - π x^{3} + π^{2} x^{2} - π^{3} x + π^{4}) (x^{4} + π x^{3} + π^{2} x^{2} + π^{3} x + π^{4}))

Plug in the value

x = π

= (π + π) (π^{4} - π π^{3} + π^{2} π^{2} - π^{3} π + π^{4}) (π^{4} + π π^{3} + π^{2} π^{2} + π^{3} π + π^{4})

Simplify

(π + π) (π^{4} - π π^{3} + π^{2} π^{2} - π^{3} π + π^{4}) (π^{4} + π π^{3} + π^{2} π^{2} + π^{3} π + π^{4}) : 10 π^{9}

= 10 π^{9}

\int x 5 - x d x

f (x) = ln (4^{x} + 8^{x})

\int 12 \cdot (2 x + 7) \cdot (x + 1)^{2} d x

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

\frac{d}{d x} (- 2^{- x})

What is the limit as x approaches pi of ((x^{10}-pi^{10}))/(x-pi) ?
The limit as x approaches pi of ((x^{10}-pi^{10}))/(x-pi) is 10pi^9