Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (1+3*x)^(5/x)
-
Limit of x^2/(-2+sqrt(4+x^2))
-
Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
- Graphing y =:
- 4*sin(3*x)
- Integral of d{x}:
- 4*sin(3*x)
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Identical expressions
- four *sin(three *x)
- 4 multiply by sinus of (3 multiply by x)
- four multiply by sinus of (three multiply by x)
- 4sin(3x)
- 4sin3x
Limit of the function 4*sin(3*x)
The solution
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lim (4*sin(3*x)) x->0+
$$\lim_{x \to 0^+}\left(4 \sin{\left(3 x \right)}\right)$$
Limit(4*sin(3*x), x, 0)
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
$$\lim_{x \to 0^-}\left(4 \sin{\left(3 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sin{\left(3 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(4 \sin{\left(3 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(4 \sin{\left(3 x \right)}\right) = 4 \sin{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sin{\left(3 x \right)}\right) = 4 \sin{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \sin{\left(3 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sin{\left(3 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(4 \sin{\left(3 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(4 \sin{\left(3 x \right)}\right) = 4 \sin{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sin{\left(3 x \right)}\right) = 4 \sin{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \sin{\left(3 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→-oo
One‐sided limits
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lim (4*sin(3*x)) x->0+
$$\lim_{x \to 0^+}\left(4 \sin{\left(3 x \right)}\right)$$
0
$$0$$
= 8.53202382582053e-30
lim (4*sin(3*x)) x->0-
$$\lim_{x \to 0^-}\left(4 \sin{\left(3 x \right)}\right)$$
0
$$0$$
= -8.53202382582053e-30
= -8.53202382582053e-30
The graph