Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-2+x^2-x)/(-2-3*x+2*x^2)
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Limit of (-20+x^2-x)/(12+x^2+7*x)
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Limit of ((1+x+x^2)/(x^2+3*x))^(-5+4*x)
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Limit of 1+2/x+3*x
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Identical expressions
- x^(eight / fifteen)*sin(x^ two)/(one +x)
- x to the power of (8 divide by 15) multiply by sinus of (x squared ) divide by (1 plus x)
- x to the power of (eight divide by fifteen) multiply by sinus of (x to the power of two) divide by (one plus x)
- x(8/15)*sin(x2)/(1+x)
- x8/15*sinx2/1+x
- x^(8/15)*sin(x²)/(1+x)
- x to the power of (8/15)*sin(x to the power of 2)/(1+x)
- x^(8/15)sin(x^2)/(1+x)
- x(8/15)sin(x2)/(1+x)
- x8/15sinx2/1+x
- x^8/15sinx^2/1+x
- x^(8 divide by 15)*sin(x^2) divide by (1+x)
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Similar expressions
- x^(8/15)*sin(x^2)/(1-x)
Limit of the function x^(8/15)*sin(x^2)/(1+x)
The solution
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[src]
/ 8/15 / 2\\
|x *sin\x /|
lim |-------------|
x->oo\ 1 + x /
$$\lim_{x \to \infty}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right)$$
Limit((x^(8/15)*sin(x^2))/(1 + 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
$$\lim_{x \to \infty}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = \frac{\sin{\left(1 \right)}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = \frac{\sin{\left(1 \right)}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = \frac{\sin{\left(1 \right)}}{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = \frac{\sin{\left(1 \right)}}{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{\frac{8}{15}} \sin{\left(x^{2} \right)}}{x + 1}\right) = 0$$
More at x→-oo
The graph