What is the limit as h approaches 0 of h/(e^h-1) ?

The limit as h approaches 0 of h/(e^h-1) is 1

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limit as h approaches 0 of h/(e^h-1)

h \to 0 lim (\frac{h}{e ^{h} - 1})

1

Solution steps

h \to 0 lim (\frac{h}{e ^{h} - 1})

Apply L'Hopital's Rule

: h \to 0 lim (\frac{1}{e ^{h}})

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

Plug in the value

h = 0

= \frac{1}{e ^{0}}

Simplify

= 1

x \to - 3 lim (\frac{x ^{2} - 2}{x + 1})

x \to 0 - lim ((1 - e^{x})^{2 x})

x \to 5 lim (\frac{x}{x ^{2} + 1})

x \to 0 lim (\frac{3 x - 1}{x - 2})

x \to - 1 lim (5 x^{3} - x^{2} + 3 x + 7)

What is the limit as h approaches 0 of h/(e^h-1) ?
The limit as h approaches 0 of h/(e^h-1) is 1