Mister Exam
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How to use it?
- Limit of the function:
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Limit of (2+sqrt(x)-sqrt(2))/x
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Limit of (2-x)/(-1+x)^2
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Limit of e^(x^2)-cos(x)/x^2
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Limit of (-44-x+3*x^2)/(-16+x^2)
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Identical expressions
- - ten +x^ three - one hundred and twenty-five *x/ two
- minus 10 plus x cubed minus 125 multiply by x divide by 2
- minus ten plus x to the power of three minus one hundred and twenty minus five multiply by x divide by two
- -10+x3-125*x/2
- -10+x³-125*x/2
- -10+x to the power of 3-125*x/2
- -10+x^3-125x/2
- -10+x3-125x/2
- -10+x^3-125*x divide by 2
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Similar expressions
- 10+x^3-125*x/2
- -10-x^3-125*x/2
- -10+x^3+125*x/2
Limit of the function -10+x^3-125*x/2
The solution
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[src]
/ 3 125*x\ lim |-10 + x - -----| x->5+\ 2 /
$$\lim_{x \to 5^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right)$$
Limit(-10 + x^3 - 125*x/2, x, 5)
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]
/ 3 125*x\ lim |-10 + x - -----| x->5+\ 2 /
$$\lim_{x \to 5^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right)$$
-395/2
$$- \frac{395}{2}$$
= -197.5
/ 3 125*x\ lim |-10 + x - -----| x->5-\ 2 /
$$\lim_{x \to 5^-}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right)$$
-395/2
$$- \frac{395}{2}$$
= -197.5
= -197.5
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 5^-}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{395}{2}$$
More at x→5 from the left
$$\lim_{x \to 5^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{395}{2}$$
$$\lim_{x \to \infty}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = -10$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = -10$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{143}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{143}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = -\infty$$
More at x→-oo
More at x→5 from the left
$$\lim_{x \to 5^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{395}{2}$$
$$\lim_{x \to \infty}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = -10$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = -10$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{143}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = - \frac{143}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{125 x}{2} + \left(x^{3} - 10\right)\right) = -\infty$$
More at x→-oo
The graph