Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-16+x^2-6*x)/(-2+x+x^2)
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Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
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Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
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Limit of cos((1+x)/x^3)
- Derivative of:
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x^(7/6)
- Integral of d{x}:
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x^(7/6)
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Identical expressions
- x^(seven / six)
- x to the power of (7 divide by 6)
- x to the power of (seven divide by six)
- x(7/6)
- x7/6
- x^7/6
- x^(7 divide by 6)
Limit of the function x^(7/6)
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]
7/6 lim x x->-1+
$$\lim_{x \to -1^+} x^{\frac{7}{6}}$$
6 ____ -\/ -1
$$- \sqrt[6]{-1}$$
= (-0.866025403784439 - 0.5j)
7/6 lim x x->-1-
$$\lim_{x \to -1^-} x^{\frac{7}{6}}$$
6 ____ -\/ -1
$$- \sqrt[6]{-1}$$
= (-0.866025403784439 - 0.5j)
= (-0.866025403784439 - 0.5j)
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -1^-} x^{\frac{7}{6}} = - \sqrt[6]{-1}$$
More at x→-1 from the left
$$\lim_{x \to -1^+} x^{\frac{7}{6}} = - \sqrt[6]{-1}$$
$$\lim_{x \to \infty} x^{\frac{7}{6}} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} x^{\frac{7}{6}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{\frac{7}{6}} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{\frac{7}{6}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{\frac{7}{6}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{\frac{7}{6}} = - \infty \sqrt[6]{-1}$$
More at x→-oo
More at x→-1 from the left
$$\lim_{x \to -1^+} x^{\frac{7}{6}} = - \sqrt[6]{-1}$$
$$\lim_{x \to \infty} x^{\frac{7}{6}} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} x^{\frac{7}{6}} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} x^{\frac{7}{6}} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} x^{\frac{7}{6}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} x^{\frac{7}{6}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} x^{\frac{7}{6}} = - \infty \sqrt[6]{-1}$$
More at x→-oo
The graph