What is the limit as h approaches 0 of (|3+h|-|3|)/h ?

The limit as h approaches 0 of (|3+h|-|3|)/h is 1

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limit as h approaches 0 of (|3+h|-|3|)/h

h \to 0 lim (\frac{∣ 3 + h ∣ - ∣ 3 ∣}{h})

1

Solution steps

h \to 0 lim (\frac{∣ 3 + h ∣ - ∣ 3 ∣}{h})

3 + h

is positive when

h \to 0

. Therefore

∣ 3 + h ∣ = 3 + h

= h \to 0 lim (\frac{3 + h - ∣ 3 ∣}{h})

3

is positive when

h \to 0

. Therefore

∣ 3 ∣ = 3

= h \to 0 lim (\frac{3 + h - 3}{h})

Simplify

= h \to 0 lim (1)

x \to a lim c = c

= 1

\frac{d}{d x} (x - ∣ ln ∣ x ∣ ∣)

\frac{\partial}{\partial y} (x^{3} y + e^{x})

x^{^{'}} = x^{\frac{4}{5}}

\int_{0}^{1} x^{1} e^{- x^{2}} d x

\frac{d}{d x} (2 x^{7} - x^{5} + 5 x^{3} - 8 x + 4)

What is the limit as h approaches 0 of (|3+h|-|3|)/h ?
The limit as h approaches 0 of (|3+h|-|3|)/h is 1