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e^x/(1+x)
Limit of the function/ e^x/(1+x)

Limit of the function e^x/(1+x)

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The solution

You have entered [src] 
      /   x \
      |  E  |
 lim  |-----|
x->-1+\1 + x/
lim⁡x→−1+(exx+1)\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right) 
Limit(E^x/(1 + x), x, -1)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
-2.0-1.5-1.0-0.52.00.00.51.01.5-50100
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→−1−(exx+1)=∞\lim_{x \to -1^-}\left(\frac{e^{x}}{x + 1}\right) = \infty
More at x→-1 from the left
lim⁡x→−1+(exx+1)=∞\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right) = \infty
lim⁡x→∞(exx+1)=∞\lim_{x \to \infty}\left(\frac{e^{x}}{x + 1}\right) = \infty
More at x→oo
lim⁡x→0−(exx+1)=1\lim_{x \to 0^-}\left(\frac{e^{x}}{x + 1}\right) = 1
More at x→0 from the left
lim⁡x→0+(exx+1)=1\lim_{x \to 0^+}\left(\frac{e^{x}}{x + 1}\right) = 1
More at x→0 from the right
lim⁡x→1−(exx+1)=e2\lim_{x \to 1^-}\left(\frac{e^{x}}{x + 1}\right) = \frac{e}{2}
More at x→1 from the left
lim⁡x→1+(exx+1)=e2\lim_{x \to 1^+}\left(\frac{e^{x}}{x + 1}\right) = \frac{e}{2}
More at x→1 from the right
lim⁡x→−∞(exx+1)=0\lim_{x \to -\infty}\left(\frac{e^{x}}{x + 1}\right) = 0
More at x→-oo
One‐sided limits [src] 
      /   x \
      |  E  |
 lim  |-----|
x->-1+\1 + x/
lim⁡x→−1+(exx+1)\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right) 
oo
∞\infty 
= 55.9188958954214
      /   x \
      |  E  |
 lim  |-----|
x->-1-\1 + x/
lim⁡x→−1−(exx+1)\lim_{x \to -1^-}\left(\frac{e^{x}}{x + 1}\right) 
-oo
−∞-\infty 
= -55.1831316349482
= -55.1831316349482
Rapid solution [src] 
oo
∞\infty
Expand and simplify
Numerical answer [src] 
55.9188958954214
55.9188958954214
The graph
Limit of the function e^x/(1+x)
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