Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(x)/x+tan(x)
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Limit of x*tan(2*x)/3
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Limit of x^2*tan(2*x)/2
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Limit of sqrt(n^2+2*n)-sqrt(3+n^2-2*n)
- Derivative of:
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sin(x)/x^5
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Identical expressions
- sin(x)/x^ five
- sinus of (x) divide by x to the power of 5
- sinus of (x) divide by x to the power of five
- sin(x)/x5
- sinx/x5
- sin(x)/x⁵
- sinx/x^5
- sin(x) divide by x^5
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Similar expressions
- (-x+e^x*sin(x))/(x^5+3*x^2)
- sinx/x^5
Limit of the function sin(x)/x^5
The solution
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[src]
/sin(x)\
lim |------|
x->oo| 5 |
\ x /
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right)$$
Limit(sin(x)/(x^5), 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
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{x^{5}}\right) = 0$$
More at x→-oo
The graph