Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-5+2*x^2+3*x)/(-1+x^2)
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Limit of (-1+2*e^(-2+x))^((2+3*x)/(-2+x))
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Limit of (1/x)^atan(2*x)
- Limit of (1-x)/(1-sin(p*x/2))
- Graphing y =:
- x+e^(-x)
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Identical expressions
- x+e^(-x)
- x plus e to the power of ( minus x)
- x+e(-x)
- x+e-x
- x+e^-x
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Similar expressions
- x-e^(-x)
- -x+e^(-x)*(2+x^2+3*x)
- x+e^(x)
- (x+e^(-x)/3)/x
Limit of the function x+e^(-x)
The solution
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[src]
/ -x\ lim \x + E / x->1+
$$\lim_{x \to 1^+}\left(x + e^{- x}\right)$$
Limit(x + E^(-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
$$\lim_{x \to 1^-}\left(x + e^{- x}\right) = \frac{1 + e}{e}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + e^{- x}\right) = \frac{1 + e}{e}$$
$$\lim_{x \to \infty}\left(x + e^{- x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x + e^{- x}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + e^{- x}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(x + e^{- x}\right) = \infty$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + e^{- x}\right) = \frac{1 + e}{e}$$
$$\lim_{x \to \infty}\left(x + e^{- x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(x + e^{- x}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + e^{- x}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(x + e^{- x}\right) = \infty$$
More at x→-oo
One‐sided limits
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/ -x\ lim \x + E / x->1+
$$\lim_{x \to 1^+}\left(x + e^{- x}\right)$$
-1 (1 + E)*e
$$\frac{1 + e}{e}$$
= 1.36787944117144
/ -x\ lim \x + E / x->1-
$$\lim_{x \to 1^-}\left(x + e^{- x}\right)$$
-1 (1 + E)*e
$$\frac{1 + e}{e}$$
= 1.36787944117144
= 1.36787944117144
The graph