What is the limit as h approaches 0+of (|h|)/h+h^2 ?

The limit as h approaches 0+of (|h|)/h+h^2 is 1

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limit as h approaches 0+of (|h|)/h+h^2

h \to 0 + lim (\frac{∣ h ∣}{h} + h^{2})

1

Solution steps

h \to 0 + lim (\frac{∣ h ∣}{h} + h^{2})

h

is positive when

h \to 0 +

. Therefore

∣ h ∣ = h

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

h \to 0 + lim (\frac{h}{h}) = 1

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

= 1 + 0

Simplify

= 1

e^{f (x)}

2 x (1 - x)

\frac{d y}{d x} = \frac{8 x}{3 y}

x \to 0 lim (arcsin (x^{3}))

\int \frac{sin ( \frac{8}{x} )}{x ^{2}} d x

What is the limit as h approaches 0+of (|h|)/h+h^2 ?
The limit as h approaches 0+of (|h|)/h+h^2 is 1