What is the limit as k approaches 0 of ((2z+3k)^3-4k^2z)/(2z(2z-k)^2) ?

The limit as k approaches 0 of ((2z+3k)^3-4k^2z)/(2z(2z-k)^2) is 1

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limit as k approaches 0 of ((2z+3k)^3-4k^2z)/(2z(2z-k)^2)

k \to 0 lim (\frac{( 2 z + 3 k ) ^{3} - 4 k ^{2} z}{2 z ( 2 z - k ) ^{2}})

1

Solution steps

k \to 0 lim (\frac{( 2 z + 3 k ) ^{3} - 4 k ^{2} z}{2 z ( 2 z - k ) ^{2}})

Plug in the value

k = 0

= \frac{( 2 z + 3 \cdot 0 ) ^{3} - 4 \cdot 0 ^{2} z}{2 z ( 2 z - 0 ) ^{2}}

Simplify

\frac{( 2 z + 3 \cdot 0 ) ^{3} - 4 \cdot 0 ^{2} z}{2 z ( 2 z - 0 ) ^{2}} : 1

= 1

\int_{2}^{\infty} \frac{2}{x ^{2} - x} d x

\frac{d}{d x} (ln (x ln (x)))

\frac{d y}{d x} = 5^{x} ln (5) + \frac{2}{x ^{2} + 1}

X^{5}

y^{^{''}} + 9 y = x e^{x}

What is the limit as k approaches 0 of ((2z+3k)^3-4k^2z)/(2z(2z-k)^2) ?
The limit as k approaches 0 of ((2z+3k)^3-4k^2z)/(2z(2z-k)^2) is 1