Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-1+3*x)/(5+x^2+7*x)
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Limit of (7+x+x^2)/(-1+e^x)
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Limit of x^2/(-2+sqrt(4+x^2))
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Limit of (x^2-6*x)/(6+x^2-7*x)
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Identical expressions
- - two + five *x+ fourteen *x^ two / three
- minus 2 plus 5 multiply by x plus 14 multiply by x squared divide by 3
- minus two plus five multiply by x plus fourteen multiply by x to the power of two divide by three
- -2+5*x+14*x2/3
- -2+5*x+14*x²/3
- -2+5*x+14*x to the power of 2/3
- -2+5x+14x^2/3
- -2+5x+14x2/3
- -2+5*x+14*x^2 divide by 3
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Similar expressions
- -2+5*x-14*x^2/3
- -2-5*x+14*x^2/3
- 2+5*x+14*x^2/3
Limit of the function -2+5*x+14*x^2/3
The solution
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[src]
/ 2\
| 14*x |
lim |-2 + 5*x + -----|
x->-1+\ 3 /
$$\lim_{x \to -1^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right)$$
Limit(-2 + 5*x + (14*x^2)/3, x, -1)
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\
| 14*x |
lim |-2 + 5*x + -----|
x->-1+\ 3 /
$$\lim_{x \to -1^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right)$$
-7/3
$$- \frac{7}{3}$$
= -2.33333333333333
/ 2\
| 14*x |
lim |-2 + 5*x + -----|
x->-1-\ 3 /
$$\lim_{x \to -1^-}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right)$$
-7/3
$$- \frac{7}{3}$$
= -2.33333333333333
= -2.33333333333333
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -1^-}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = - \frac{7}{3}$$
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = - \frac{7}{3}$$
$$\lim_{x \to \infty}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = -2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = -2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \frac{23}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \frac{23}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \infty$$
More at x→-oo
More at x→-1 from the left
$$\lim_{x \to -1^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = - \frac{7}{3}$$
$$\lim_{x \to \infty}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = -2$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = -2$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \frac{23}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \frac{23}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{14 x^{2}}{3} + \left(5 x - 2\right)\right) = \infty$$
More at x→-oo
The graph