What is the limit as x approaches 0 of (13e^{2x}-13)/(e^x-1) ?

The limit as x approaches 0 of (13e^{2x}-13)/(e^x-1) is 26

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limit as x approaches 0 of (13e^{2x}-13)/(e^x-1)

x \to 0 lim (\frac{13 e ^{2 x} - 13}{e ^{x} - 1})

26

Solution steps

x \to 0 lim (\frac{13 e ^{2 x} - 13}{e ^{x} - 1})

Simplify

\frac{13 e ^{2 x} - 13}{e ^{x} - 1} : 13 (e^{x} + 1)

= x \to 0 lim (13 (e^{x} + 1))

Plug in the value

x = 0

= 13 (e^{0} + 1)

Simplify

= 26

x \to 0 + lim (cos^{\frac{9}{x ^{2}}} (x))

h \to 0 lim (\frac{( 2 + h ) ^{4 + h} - 16}{h})

x \to 2 lim (x^{2} - 4 x + 1)

x \to 16 lim (\frac{x ^{3} - 2 x ^{2} - 3 x}{x + 5 - 2})

x \to 5 lim (\frac{x ^{2} - 5 x}{x - 10})

What is the limit as x approaches 0 of (13e^{2x}-13)/(e^x-1) ?
The limit as x approaches 0 of (13e^{2x}-13)/(e^x-1) is 26