Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (5+x-3*x^2)/(4-x+2*x^2)
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Limit of (4-x^2)/(3-x^2)
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Limit of (3+2*x)/(1-5*x)
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Limit of (1-2*cos(x))/sin(3*x)
- Integral of d{x}:
- 3^(-x)
- Graphing y =:
- 3^(-x)
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Identical expressions
- three ^(-x)
- 3 to the power of ( minus x)
- three to the power of ( minus x)
- 3(-x)
- 3-x
- 3^-x
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Similar expressions
- sin(2*pi*3^(-x))
- (-2+3^x+3^(-x))/x^2
- 2/3-3^(-x)-2^x/3
- 3^(x)
- (3^x-3^(-x))/(3^x+3^(-x))
Limit of the function 3^(-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]
-x lim 3 x->2+
$$\lim_{x \to 2^+} 3^{- x}$$
1/9
$$\frac{1}{9}$$
= 0.111111111111111
-x lim 3 x->2-
$$\lim_{x \to 2^-} 3^{- x}$$
1/9
$$\frac{1}{9}$$
= 0.111111111111111
= 0.111111111111111
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-} 3^{- x} = \frac{1}{9}$$
More at x→2 from the left
$$\lim_{x \to 2^+} 3^{- x} = \frac{1}{9}$$
$$\lim_{x \to \infty} 3^{- x} = 0$$
More at x→oo
$$\lim_{x \to 0^-} 3^{- x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} 3^{- x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} 3^{- x} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} 3^{- x} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} 3^{- x} = \infty$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+} 3^{- x} = \frac{1}{9}$$
$$\lim_{x \to \infty} 3^{- x} = 0$$
More at x→oo
$$\lim_{x \to 0^-} 3^{- x} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} 3^{- x} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} 3^{- x} = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+} 3^{- x} = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty} 3^{- x} = \infty$$
More at x→-oo
The graph