Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+x^2+3*x)/(2+2*x^2+5*x)
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Limit of (-51+x^2-14*x)/(-21+x^2-4*x)
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Limit of -sec(x)+tan(x)
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Limit of tan(3*x)/(4*x)
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Identical expressions
- -x^ two / two +cos(x)
- minus x squared divide by 2 plus co sinus of e of (x)
- minus x to the power of two divide by two plus co sinus of e of (x)
- -x2/2+cos(x)
- -x2/2+cosx
- -x²/2+cos(x)
- -x to the power of 2/2+cos(x)
- -x^2/2+cosx
- -x^2 divide by 2+cos(x)
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Similar expressions
- x^2/2+cos(x)
- -x^2/2-cos(x)
- -x^2/2+cosx
Limit of the function -x^2/2+cos(x)
The solution
You have entered
[src]
/ 2 \
|-x |
lim |---- + cos(x)|
x->0+\ 2 /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right)$$
Limit((-x^2)/2 + cos(x), x, 0)
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = - \frac{1}{2} + \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = - \frac{1}{2} + \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = - \frac{1}{2} + \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = - \frac{1}{2} + \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
|-x |
lim |---- + cos(x)|
x->0+\ 2 /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right)$$
1
$$1$$
= 1.0
/ 2 \
|-x |
lim |---- + cos(x)|
x->0-\ 2 /
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) x^{2}}{2} + \cos{\left(x \right)}\right)$$
1
$$1$$
= 1.0
= 1.0
The graph