Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of -1+(-1+x)^2/x^2
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Limit of e^(-x)*x^100
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Limit of (4*x^2+tan(3*x))/asin(8*x)
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Limit of -7+x+sqrt(2)-3/x
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Identical expressions
- - seven +x+sqrt(two)- three /x
- minus 7 plus x plus square root of (2) minus 3 divide by x
- minus seven plus x plus square root of (two) minus three divide by x
- -7+x+√(2)-3/x
- -7+x+sqrt2-3/x
- -7+x+sqrt(2)-3 divide by x
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Similar expressions
- -7+x+sqrt(2)+3/x
- 7+x+sqrt(2)-3/x
- -7+x-sqrt(2)-3/x
- -7-x+sqrt(2)-3/x
Limit of the function -7+x+sqrt(2)-3/x
The solution
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[src]
/ ___ 3\ lim |-7 + x + \/ 2 - -| x->7+\ x/
$$\lim_{x \to 7^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right)$$
Limit(-7 + x + sqrt(2) - 3/x, x, 7)
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]
/ ___ 3\ lim |-7 + x + \/ 2 - -| x->7+\ x/
$$\lim_{x \to 7^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right)$$
3 ___ - - + \/ 2 7
$$- \frac{3}{7} + \sqrt{2}$$
= 0.985642133801666
/ ___ 3\ lim |-7 + x + \/ 2 - -| x->7-\ x/
$$\lim_{x \to 7^-}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right)$$
3 ___ - - + \/ 2 7
$$- \frac{3}{7} + \sqrt{2}$$
= 0.985642133801666
= 0.985642133801666
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 7^-}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = - \frac{3}{7} + \sqrt{2}$$
More at x→7 from the left
$$\lim_{x \to 7^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = - \frac{3}{7} + \sqrt{2}$$
$$\lim_{x \to \infty}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -9 + \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -9 + \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -\infty$$
More at x→-oo
More at x→7 from the left
$$\lim_{x \to 7^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = - \frac{3}{7} + \sqrt{2}$$
$$\lim_{x \to \infty}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -9 + \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -9 + \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\left(x - 7\right) + \sqrt{2}\right) - \frac{3}{x}\right) = -\infty$$
More at x→-oo
The graph