Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
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Limit of (-tan(2*x)+sin(2*x))/x^3
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Limit of 3/n^4
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Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
- Canonical form:
- 1+sin(x)
- Derivative of:
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1+sin(x)
- Integral of d{x}:
- 1+sin(x)
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Identical expressions
- one +sin(x)
- 1 plus sinus of (x)
- one plus sinus of (x)
- 1+sinx
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Similar expressions
- 1-sin(x)
- 1+sinx
Limit of the function 1+sin(x)
The solution
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lim (1 + sin(x)) x->0+
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} + 1\right)$$
Limit(1 + sin(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
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} + 1\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} + 1\right) = \sin{\left(1 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} + 1\right) = \sin{\left(1 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} + 1\right) = 1$$
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} + 1\right) = \sin{\left(1 \right)} + 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} + 1\right) = \sin{\left(1 \right)} + 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} + 1\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
One‐sided limits
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lim (1 + sin(x)) x->0+
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} + 1\right)$$
1
$$1$$
= 1
lim (1 + sin(x)) x->0-
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} + 1\right)$$
1
$$1$$
= 1
= 1
The graph