Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-2*x+5*x^2)/(-3+x+2*x^2)
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Limit of (-asin(x)+2*x)/(2*x+acot(x))
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Limit of (1+2*x^2+5*x)/(-3+x^2+2*x)
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Limit of (x^2-x)/(-7+2*x^2+5*x)
- Graphing y =:
- 1+sin(2*x)
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Identical expressions
- one +sin(two *x)
- 1 plus sinus of (2 multiply by x)
- one plus sinus of (two multiply by x)
- 1+sin(2x)
- 1+sin2x
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Similar expressions
- 1-sin(2*x)
Limit of the function 1+sin(2*x)
The solution
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lim (1 + sin(2*x)) x->0+
$$\lim_{x \to 0^+}\left(\sin{\left(2 x \right)} + 1\right)$$
Limit(1 + sin(2*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
One‐sided limits
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lim (1 + sin(2*x)) x->0+
$$\lim_{x \to 0^+}\left(\sin{\left(2 x \right)} + 1\right)$$
1
$$1$$
= 1.0
lim (1 + sin(2*x)) x->0-
$$\lim_{x \to 0^-}\left(\sin{\left(2 x \right)} + 1\right)$$
1
$$1$$
= 1.0
= 1.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\sin{\left(2 x \right)} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(2 x \right)} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(\sin{\left(2 x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sin{\left(2 x \right)} + 1\right) = \sin{\left(2 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(2 x \right)} + 1\right) = \sin{\left(2 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(2 x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(2 x \right)} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(\sin{\left(2 x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sin{\left(2 x \right)} + 1\right) = \sin{\left(2 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(2 x \right)} + 1\right) = \sin{\left(2 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(2 x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
The graph