Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x*cos(x)
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Limit of e^(2*x)
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Limit of sin(6*pi*x)/sin(pi*x)
- Limit of cos(x)/factorial(x)
- Integral of d{x}:
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e^(2*x)
- Derivative of:
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e^(2*x)
- Equation:
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e^(2*x)
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Identical expressions
- e^(two *x)
- e to the power of (2 multiply by x)
- e to the power of (two multiply by x)
- e(2*x)
- e2*x
- e^(2x)
- e(2x)
- e2x
- e^2x
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Similar expressions
- (e^(4*x)-e^(2*x))/x
- x*sin(x)/(-1+e^(2*x))
- sin(6*x)/(-1+e^(2*x))
- atan(4*x)/(-1+e^(2*x))
Limit of the function e^(2*x)
The solution
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
One‐sided limits
[src]
2*x lim E x->1+
$$\lim_{x \to 1^+} e^{2 x}$$
2 e
$$e^{2}$$
= 7.38905609893065
2*x lim E x->1-
$$\lim_{x \to 1^-} e^{2 x}$$
2 e
$$e^{2}$$
= 7.38905609893065
= 7.38905609893065
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-} e^{2 x} = e^{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} e^{2 x} = e^{2}$$
$$\lim_{x \to \infty} e^{2 x} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} e^{2 x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{2 x} = 1$$
More at x→0 from the right
$$\lim_{x \to -\infty} e^{2 x} = 0$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+} e^{2 x} = e^{2}$$
$$\lim_{x \to \infty} e^{2 x} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} e^{2 x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} e^{2 x} = 1$$
More at x→0 from the right
$$\lim_{x \to -\infty} e^{2 x} = 0$$
More at x→-oo
The graph