limit as x approaches 4 of (x^4-256)/(x^3-64)

解答

x \to 4 lim (\frac{x ^{4} - 256}{x ^{3} - 64})

\frac{16}{3}

十进制

5.33333 \dots

求解步骤

x \to 4 lim (\frac{x ^{4} - 256}{x ^{3} - 64})

化简

\frac{x ^{4} - 256}{x ^{3} - 64} : \frac{( x ^{2} + 16 ) ( x + 4 )}{x ^{2} + 4 x + 16}

= x \to 4 lim (\frac{( x ^{2} + 16 ) ( x + 4 )}{x ^{2} + 4 x + 16})

代入值

x = 4

= \frac{( 4 ^{2} + 16 ) ( 4 + 4 )}{4 ^{2} + 4 \cdot 4 + 16}

化简

\frac{( 4 ^{2} + 16 ) ( 4 + 4 )}{4 ^{2} + 4 \cdot 4 + 16} : \frac{16}{3}

= \frac{16}{3}

ma c l a u r in (1 + x^{2})^{- \frac{3}{2}}

a re a f (x) = \frac{7}{x}, x = 1, x = 41

x \to 3 + lim (\frac{6 x}{x ^{2} - 9})

l a pl a ce t r an s f or m t sin (t)

\int_{0}^{\infty} x^{2} d x