Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
-
Limit of (-tan(2*x)+sin(2*x))/x^3
-
Limit of 3/n^4
-
Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
- Integral of d{x}:
- sqrt(x)*sin(x^2)
-
Identical expressions
- sqrt(x)*sin(x^ two)
- square root of (x) multiply by sinus of (x squared )
- square root of (x) multiply by sinus of (x to the power of two)
- √(x)*sin(x^2)
- sqrt(x)*sin(x2)
- sqrtx*sinx2
- sqrt(x)*sin(x²)
- sqrt(x)*sin(x to the power of 2)
- sqrt(x)sin(x^2)
- sqrt(x)sin(x2)
- sqrtxsinx2
- sqrtxsinx^2
Limit of the function sqrt(x)*sin(x^2)
The solution
You have entered
[src]
/ ___ / 2\\ lim \\/ x *sin\x // x->oo
$$\lim_{x \to \infty}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right)$$
Limit(sqrt(x)*sin(x^2), 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
$$\lim_{x \to \infty}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \left\langle -\infty, \infty\right\rangle i$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sqrt{x} \sin{\left(x^{2} \right)}\right) = \left\langle -\infty, \infty\right\rangle i$$
More at x→-oo
The graph