Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
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Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
- Derivative of:
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1/sqrt(1+x)
- Integral of d{x}:
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1/sqrt(1+x)
- Sum of series:
- 1/sqrt(1+x)
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Identical expressions
- one /sqrt(one +x)
- 1 divide by square root of (1 plus x)
- one divide by square root of (one plus x)
- 1/√(1+x)
- 1/sqrt1+x
- 1 divide by sqrt(1+x)
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Similar expressions
- 1/sqrt(1-x)
- 1/sqrt(1+x^2)
- 1/(sqrt(1+x)-sqrt(-3+x))
- 1/(sqrt(1+x)-sqrt(7-x))
Limit of the function 1/sqrt(1+x)
The solution
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1
lim ---------
x->oo _______
\/ 1 + x
$$\lim_{x \to \infty} \frac{1}{\sqrt{x + 1}}$$
Limit(1/(sqrt(1 + x)), x, 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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \frac{1}{\sqrt{x + 1}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{\sqrt{x + 1}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\sqrt{x + 1}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\sqrt{x + 1}} = \frac{\sqrt{2}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\sqrt{x + 1}} = \frac{\sqrt{2}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\sqrt{x + 1}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{\sqrt{x + 1}} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{\sqrt{x + 1}} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{\sqrt{x + 1}} = \frac{\sqrt{2}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{\sqrt{x + 1}} = \frac{\sqrt{2}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{\sqrt{x + 1}} = 0$$
More at x→-oo
The graph