Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+sqrt(1+4*x))/(-2+x)
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Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
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Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
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Limit of (-1+x+6*x^2)/(1/2+x)
- Graphing y =:
- 4*sin(4*x)
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Identical expressions
- four *sin(four *x)
- 4 multiply by sinus of (4 multiply by x)
- four multiply by sinus of (four multiply by x)
- 4sin(4x)
- 4sin4x
Limit of the function 4*sin(4*x)
The solution
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lim (4*sin(4*x)) x->0+
$$\lim_{x \to 0^+}\left(4 \sin{\left(4 x \right)}\right)$$
Limit(4*sin(4*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
$$\lim_{x \to 0^-}\left(4 \sin{\left(4 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sin{\left(4 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(4 \sin{\left(4 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(4 \sin{\left(4 x \right)}\right) = 4 \sin{\left(4 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sin{\left(4 x \right)}\right) = 4 \sin{\left(4 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \sin{\left(4 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sin{\left(4 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(4 \sin{\left(4 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(4 \sin{\left(4 x \right)}\right) = 4 \sin{\left(4 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sin{\left(4 x \right)}\right) = 4 \sin{\left(4 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \sin{\left(4 x \right)}\right) = \left\langle -4, 4\right\rangle$$
More at x→-oo
One‐sided limits
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lim (4*sin(4*x)) x->0+
$$\lim_{x \to 0^+}\left(4 \sin{\left(4 x \right)}\right)$$
0
$$0$$
= 1.02887573293461e-29
lim (4*sin(4*x)) x->0-
$$\lim_{x \to 0^-}\left(4 \sin{\left(4 x \right)}\right)$$
0
$$0$$
= -1.02887573293461e-29
= -1.02887573293461e-29
The graph