Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-cos(3*x)
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Limit of (-10+6*x^2+7*x)/(-4+x^2)
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Limit of (7+n)/(5+n)
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Limit of -3+x*(7-6*x)^x/3
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Identical expressions
- -x^ two +(two +x)*(three +x)/ four
- minus x squared plus (2 plus x) multiply by (3 plus x) divide by 4
- minus x to the power of two plus (two plus x) multiply by (three plus x) divide by four
- -x2+(2+x)*(3+x)/4
- -x2+2+x*3+x/4
- -x²+(2+x)*(3+x)/4
- -x to the power of 2+(2+x)*(3+x)/4
- -x^2+(2+x)(3+x)/4
- -x2+(2+x)(3+x)/4
- -x2+2+x3+x/4
- -x^2+2+x3+x/4
- -x^2+(2+x)*(3+x) divide by 4
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Similar expressions
- -x^2+(2+x)*(3-x)/4
- -x^2+(2-x)*(3+x)/4
- x^2+(2+x)*(3+x)/4
- -x^2-(2+x)*(3+x)/4
Limit of the function -x^2+(2+x)*(3+x)/4
The solution
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[src]
/ 2 (2 + x)*(3 + x)\ lim |- x + ---------------| x->-2+\ 4 /
$$\lim_{x \to -2^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right)$$
Limit(-x^2 + ((2 + x)*(3 + x))/4, x, -2)
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)*(3 + x)\ lim |- x + ---------------| x->-2+\ 4 /
$$\lim_{x \to -2^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right)$$
-4
$$-4$$
= -4.0
/ 2 (2 + x)*(3 + x)\ lim |- x + ---------------| x->-2-\ 4 /
$$\lim_{x \to -2^-}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right)$$
-4
$$-4$$
= -4.0
= -4.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -2^-}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -4$$
More at x→-2 from the left
$$\lim_{x \to -2^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -4$$
$$\lim_{x \to \infty}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = \frac{3}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = \frac{3}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -\infty$$
More at x→-oo
More at x→-2 from the left
$$\lim_{x \to -2^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -4$$
$$\lim_{x \to \infty}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = \frac{3}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = \frac{3}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2} + \frac{\left(x + 2\right) \left(x + 3\right)}{4}\right) = -\infty$$
More at x→-oo
The graph