Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Graphing y =:
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e^x/(1+x)
- Integral of d{x}:
- e^x/(1+x)
- Derivative of:
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e^x/(1+x)
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Identical expressions
- e^x/(one +x)
- e to the power of x divide by (1 plus x)
- e to the power of x divide by (one plus x)
- ex/(1+x)
- ex/1+x
- e^x/1+x
- e^x divide by (1+x)
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Similar expressions
- e^x/(1-x)
Limit of the function e^x/(1+x)
The solution
You have entered
[src]
/ x \
| E |
lim |-----|
x->-1+\1 + x/
$$\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right)$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -1^-}\left(\frac{e^{x}}{x + 1}\right) = \infty$$
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{x}}{x + 1}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{e^{x}}{x + 1}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{x}}{x + 1}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{e^{x}}{x + 1}\right) = \frac{e}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{x}}{x + 1}\right) = \frac{e}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{x}}{x + 1}\right) = 0$$
More at x→-oo
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{e^{x}}{x + 1}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{e^{x}}{x + 1}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{e^{x}}{x + 1}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{e^{x}}{x + 1}\right) = \frac{e}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{e^{x}}{x + 1}\right) = \frac{e}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{e^{x}}{x + 1}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/ x \
| E |
lim |-----|
x->-1+\1 + x/
$$\lim_{x \to -1^+}\left(\frac{e^{x}}{x + 1}\right)$$
oo
$$\infty$$
= 55.9188958954214
/ x \
| E |
lim |-----|
x->-1-\1 + x/
$$\lim_{x \to -1^-}\left(\frac{e^{x}}{x + 1}\right)$$
-oo
$$-\infty$$
= -55.1831316349482
= -55.1831316349482
The graph