Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (5-4*x+3*x^2)/(1-x+2*x^2)
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Limit of ((1+2*x)/(-1+x))^(4*x)
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Limit of (4+x^2-5*x)/(-16+x^2)
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Limit of sinh(x)/x
- Derivative of:
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cos(x)+sin(x)
- Graphing y =:
- cos(x)+sin(x)
- Canonical form:
- cos(x)+sin(x)
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Identical expressions
- cos(x)+sin(x)
- co sinus of e of (x) plus sinus of (x)
- cosx+sinx
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Similar expressions
- cos(x)-sin(x)
- cosx+sinx
Limit of the function cos(x)+sin(x)
The solution
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[src]
lim (cos(x) + sin(x)) pi x->--+ 6
$$\lim_{x \to \frac{\pi}{6}^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
Limit(cos(x) + sin(x), x, pi/6)
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
$$\lim_{x \to \frac{\pi}{6}^-}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \frac{1}{2} + \frac{\sqrt{3}}{2}$$
More at x→pi/6 from the left
$$\lim_{x \to \frac{\pi}{6}^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \frac{1}{2} + \frac{\sqrt{3}}{2}$$
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
More at x→pi/6 from the left
$$\lim_{x \to \frac{\pi}{6}^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \frac{1}{2} + \frac{\sqrt{3}}{2}$$
$$\lim_{x \to \infty}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \cos{\left(1 \right)} + \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
One‐sided limits
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lim (cos(x) + sin(x)) pi x->--+ 6
$$\lim_{x \to \frac{\pi}{6}^+}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
___ 1 \/ 3 - + ----- 2 2
$$\frac{1}{2} + \frac{\sqrt{3}}{2}$$
= 1.36602540378444
lim (cos(x) + sin(x)) pi x->--- 6
$$\lim_{x \to \frac{\pi}{6}^-}\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
___ 1 \/ 3 - + ----- 2 2
$$\frac{1}{2} + \frac{\sqrt{3}}{2}$$
= 1.36602540378444
= 1.36602540378444
The graph