Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+x^2+3*x)/(2+2*x^2+5*x)
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Limit of -sec(x)+tan(x)
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Limit of (asin(x)^2-atan(x)^2+sin(2*x))/(3*x)
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Limit of 1+(4/3)^n
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Identical expressions
- one +(four / three)^n
- 1 plus (4 divide by 3) to the power of n
- one plus (four divide by three) to the power of n
- 1+(4/3)n
- 1+4/3n
- 1+4/3^n
- 1+(4 divide by 3)^n
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Similar expressions
- 1-(4/3)^n
Limit of the function 1+(4/3)^n
The solution
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/ n\ lim \1 + 4/3 / n->oo
$$\lim_{n \to \infty}\left(\left(\frac{4}{3}\right)^{n} + 1\right)$$
Limit(1 + (4/3)^n, n, oo, dir='-')
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 n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = \infty$$
$$\lim_{n \to 0^-}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = 2$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = 2$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = \frac{7}{3}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = \frac{7}{3}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = 1$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = 2$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = 2$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = \frac{7}{3}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = \frac{7}{3}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\left(\frac{4}{3}\right)^{n} + 1\right) = 1$$
More at n→-oo
The graph