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Popular >

limit as x approaches 0 of (2+1/(e^x))/(1+e^{4/x)}+(sin(x))/(|x|)

Solution

x \to 0 lim (\frac{2 + \frac{1}{e ^{x}}}{1 + e ^{\frac{4}{x}}} + \frac{sin ( x )}{∣ x ∣})

Solution

diverges

Solution steps

x \to 0 lim (\frac{2 + \frac{1}{e ^{x}}}{1 + e ^{\frac{4}{x}}} + \frac{sin ( x )}{∣ x ∣})

If

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (\frac{2 + \frac{1}{e ^{x}}}{1 + e ^{\frac{4}{x}}} + \frac{sin ( x )}{∣ x ∣}) = 1

x \to 0 - lim (\frac{2 + \frac{1}{e ^{x}}}{1 + e ^{\frac{4}{x}}} + \frac{sin ( x )}{∣ x ∣}) = 2

= diverges

Graph

Popular Examples

limit as x approaches-infinity of (5x^6-1)/(x^3-4)

x \to - \infty lim (\frac{5 x ^{6} - 1}{x ^{3} - 4})

limit as x approaches infinity of (n-1)!

x \to \infty lim ((n - 1)!)

limit as x approaches 0+of x^{4*sin(x)}

x \to 0 + lim (x^{4 \cdot s i n (x)})

limit as x approaches 4 of e^{2/((4-x))}

x \to 4 lim (e^{\frac{2}{( 4 - x )}})

limit as x approaches 9 of ((x^2-81))/(3-sqrt(x))

x \to 9 lim (\frac{( x ^{2} - 81 )}{3 - x})

Frequently Asked Questions (FAQ)

What is the limit as x approaches 0 of (2+1/(e^x))/(1+e^{4/x)}+(sin(x))/(|x|) ?
The limit as x approaches 0 of (2+1/(e^x))/(1+e^{4/x)}+(sin(x))/(|x|) is diverges