What is the limit as h approaches 0 of (((x+h)^4-x^4))/h ?

The limit as h approaches 0 of (((x+h)^4-x^4))/h is 4x^3

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

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

4 x^{3}

Solution steps

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

Simplify

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

Simplify

(2 x^{2} + 2 \cdot 0 \cdot x + 0^{2}) (0 + 2 x) : 4 x^{3}

= 4 x^{3}

\frac{d}{d x} (\frac{100}{( 100 - x )})

(4, 0), (0, 4)

\int (tan (y)) d y

\frac{d}{d t} (cos (2 t))

\frac{d}{d x} (2 cos (2 x))

What is the limit as h approaches 0 of (((x+h)^4-x^4))/h ?
The limit as h approaches 0 of (((x+h)^4-x^4))/h is 4x^3