limit as h approaches 0 of ((5+h)^4-625)/h

解答

h \to 0 lim (\frac{( 5 + h ) ^{4} - 625}{h})

500

求解步骤

h \to 0 lim (\frac{( 5 + h ) ^{4} - 625}{h})

化简

\frac{( 5 + h ) ^{4} - 625}{h} : (h^{2} + 10 h + 50) (h + 10)

= h \to 0 lim ((h^{2} + 10 h + 50) (h + 10))

代入值

h = 0

= (0^{2} + 10 \cdot 0 + 50) (0 + 10)

化简

(0^{2} + 10 \cdot 0 + 50) (0 + 10) : 500

= 500

d er i v a t i v e 3 e^{3 t}

f^{^{''}} (x) = e^{x}, f^{^{'}} (0) = 2, f (0) = 5

\int (4 x^{3} - 9 x^{2} + 16 x) x^{4} - 3 x^{3} + 8 x^{2} d x

x \to 0 lim (\frac{4 + x - 4 - x}{4 x})

x \to - \frac{π}{2} lim (- tan (0.5 x))