Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-16+x^2-6*x)/(-2+x+x^2)
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Limit of -1+sqrt(5)-x-2/(sqrt(2)-x)
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Limit of (-cos(x)^3+cos(x))/(4*x*sin(x))
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Limit of cos((1+x)/x^3)
- Graphing y =:
- cos((1+x)/x^3)
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Identical expressions
- cos((one +x)/x^ three)
- co sinus of e of ((1 plus x) divide by x cubed )
- co sinus of e of ((one plus x) divide by x to the power of three)
- cos((1+x)/x3)
- cos1+x/x3
- cos((1+x)/x³)
- cos((1+x)/x to the power of 3)
- cos1+x/x^3
- cos((1+x) divide by x^3)
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Similar expressions
- cos((1-x)/x^3)
Limit of the function cos((1+x)/x^3)
The solution
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/1 + x\
lim cos|-----|
x->oo | 3 |
\ x /
$$\lim_{x \to \infty} \cos{\left(\frac{x + 1}{x^{3}} \right)}$$
Limit(cos((1 + 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
$$\lim_{x \to \infty} \cos{\left(\frac{x + 1}{x^{3}} \right)} = 1$$
$$\lim_{x \to 0^-} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{x + 1}{x^{3}} \right)} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \left\langle -1, 1\right\rangle$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(\frac{x + 1}{x^{3}} \right)} = \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(\frac{x + 1}{x^{3}} \right)} = 1$$
More at x→-oo
The graph