Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (4+x^2)/(-6+2*x)
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Limit of ((1+x)/(1+2*x))^x
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Limit of (n/(1+n))^(5+3*n)
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Limit of (9^x-8^x)/asin(3*x)
- Integral of d{x}:
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sqrt(1+x^2)
- Derivative of:
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sqrt(1+x^2)
- Graphing y =:
- sqrt(1+x^2)
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Identical expressions
- sqrt(one +x^ two)
- square root of (1 plus x squared )
- square root of (one plus x to the power of two)
- √(1+x^2)
- sqrt(1+x2)
- sqrt1+x2
- sqrt(1+x²)
- sqrt(1+x to the power of 2)
- sqrt1+x^2
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Similar expressions
- pi^2*sqrt(1+x^2)
- (-cos(x)+cos(7*x))/(-1+sqrt(1+x^2))
- (1+4*x)/sqrt(1+x^2)
- sqrt(1-x^2)
- sqrt(1+x^2+4*x)-x
- (1-sqrt(1+x^2))/x^2
Limit of the function sqrt(1+x^2)
The solution
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lim \/ 1 + x
x->oo
$$\lim_{x \to \infty} \sqrt{x^{2} + 1}$$
Limit(sqrt(1 + x^2), 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
$$\lim_{x \to \infty} \sqrt{x^{2} + 1} = \infty$$
$$\lim_{x \to 0^-} \sqrt{x^{2} + 1} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{x^{2} + 1} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{x^{2} + 1} = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{x^{2} + 1} = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{x^{2} + 1} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \sqrt{x^{2} + 1} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{x^{2} + 1} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{x^{2} + 1} = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{x^{2} + 1} = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{x^{2} + 1} = \infty$$
More at x→-oo
The graph