Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-sin(x)+cos(x))^(1/x)
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Limit of (-cos(3)+cos(x))/(-3+x)
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Limit of (-cos(2*x)+cos(x))/x^2
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Limit of cos(3/x)^(x^3)
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Identical expressions
- cos(three /x)^(x^ three)
- co sinus of e of (3 divide by x) to the power of (x cubed )
- co sinus of e of (three divide by x) to the power of (x to the power of three)
- cos(3/x)(x3)
- cos3/xx3
- cos(3/x)^(x³)
- cos(3/x) to the power of (x to the power of 3)
- cos3/x^x^3
- cos(3 divide by x)^(x^3)
Limit of the function cos(3/x)^(x^3)
The solution
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/ 3\
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lim |cos|-||
x->oo\ \x//
$$\lim_{x \to \infty} \cos^{x^{3}}{\left(\frac{3}{x} \right)}$$
Limit(cos(3/x)^(x^3), 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
$$\lim_{x \to \infty} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = 0$$
$$\lim_{x \to 0^-} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = \cos{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = \cos{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = \cos{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = \cos{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos^{x^{3}}{\left(\frac{3}{x} \right)} = \infty$$
More at x→-oo
The graph