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

해법

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

4 x^{3}

솔루션 단계

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

\frac{( x + h ) ^{4} - x ^{4}}{h}

단순화하세요:

(2 x^{2} + 2 h x + h^{2}) (h + 2 x)

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

Plug in the value

h = 0

= (2 x^{2} + 2 \cdot 0 \cdot x + 0^{2}) (0 + 2 x)

(2 x^{2} + 2 \cdot 0 \cdot x + 0^{2}) (0 + 2 x)

간소화하다 :

4 x^{3}

= 4 x^{3}