Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (sin(3*x)^2-sin(x)^2)/x^2
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Limit of (-2+sqrt(-12+x^2))/(sqrt(4+3*x)-x)
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Limit of (-3+sqrt(4+5*x))/(-1+x)
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Limit of (-3+sqrt(1+4*x))/(-4+sqrt(10+3*x))
- Integral of d{x}:
- -x*sin(x)+cos(x)
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Identical expressions
- -x*sin(x)+cos(x)
- minus x multiply by sinus of (x) plus co sinus of e of (x)
- -xsin(x)+cos(x)
- -xsinx+cosx
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Similar expressions
- -x*sin(x)-cos(x)
- x*sin(x)+cos(x)
- -x*sinx+cosx
Limit of the function -x*sin(x)+cos(x)
The solution
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[src]
lim (-x*sin(x) + cos(x)) x->0+
$$\lim_{x \to 0^+}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
Limit((-x)*sin(x) + 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
One‐sided limits
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lim (-x*sin(x) + cos(x)) x->0+
$$\lim_{x \to 0^+}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
1
$$1$$
= 1.0
lim (-x*sin(x) + cos(x)) x->0-
$$\lim_{x \to 0^-}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
$$\lim_{x \to \infty}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
$$\lim_{x \to \infty}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph