Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6+x^2-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
- Derivative of:
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cos(4*x)
- Integral of d{x}:
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cos(4*x)
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Identical expressions
- cos(four *x)
- co sinus of e of (4 multiply by x)
- co sinus of e of (four multiply by x)
- cos(4x)
- cos4x
Limit of the function cos(4*x)
The solution
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lim cos(4*x) x->oo
$$\lim_{x \to \infty} \cos{\left(4 x \right)}$$
Limit(cos(4*x), x, oo, dir='-')
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
$$\lim_{x \to \infty} \cos{\left(4 x \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{x \to 0^-} \cos{\left(4 x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(4 x \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(4 x \right)} = \cos{\left(4 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(4 x \right)} = \cos{\left(4 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(4 x \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-} \cos{\left(4 x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(4 x \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(4 x \right)} = \cos{\left(4 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(4 x \right)} = \cos{\left(4 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(4 x \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
The graph