Mister Exam
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How to use it?
- Limit of the function:
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Limit of ((2+x)^2-(-2+x)^2)/(2+x)
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Limit of -2/7+x^2/7
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Limit of (1+x^2-2*x)/(1-4*x+3*x^2)
- Limit of (1+x^2+2*x)/(2+x^2+3*x)
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Identical expressions
- - two / seven +x^ two / seven
- minus 2 divide by 7 plus x squared divide by 7
- minus two divide by seven plus x to the power of two divide by seven
- -2/7+x2/7
- -2/7+x²/7
- -2/7+x to the power of 2/7
- -2 divide by 7+x^2 divide by 7
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Similar expressions
- 2/7+x^2/7
- -2/7-x^2/7
Limit of the function -2/7+x^2/7
The solution
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[src]
/ 2\
| 2 x |
lim |- - + --|
x->3+\ 7 7 /
$$\lim_{x \to 3^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right)$$
Limit(-2/7 + x^2/7, x, 3)
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]
/ 2\
| 2 x |
lim |- - + --|
x->3+\ 7 7 /
$$\lim_{x \to 3^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right)$$
1
$$1$$
= 1.0
/ 2\
| 2 x |
lim |- - + --|
x->3-\ 7 7 /
$$\lim_{x \to 3^-}\left(\frac{x^{2}}{7} - \frac{2}{7}\right)$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 3^-}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = 1$$
More at x→3 from the left
$$\lim_{x \to 3^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{2}{7}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{2}{7}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{1}{7}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{1}{7}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = \infty$$
More at x→-oo
More at x→3 from the left
$$\lim_{x \to 3^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{2}{7}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{2}{7}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{1}{7}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = - \frac{1}{7}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{7} - \frac{2}{7}\right) = \infty$$
More at x→-oo
The graph