Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 1-cos(3*x)
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Limit of ((6+5*x)/(-1+5*x))^((1+2*x^2)/x)
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Limit of (-3*5^(1+x)+5*2^x)/(2*5^x+100*2^x)
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Limit of (4^x-9^x)/(4^(1+x)+9^(1+x))
- Graphing y =:
- 1-cos(3*x)
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Identical expressions
- one -cos(three *x)
- 1 minus co sinus of e of (3 multiply by x)
- one minus co sinus of e of (three multiply by x)
- 1-cos(3x)
- 1-cos3x
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Similar expressions
- 1+cos(3*x)
Limit of the function 1-cos(3*x)
The solution
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lim (1 - cos(3*x)) x->0+
$$\lim_{x \to 0^+}\left(1 - \cos{\left(3 x \right)}\right)$$
Limit(1 - cos(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
$$\lim_{x \to 0^-}\left(1 - \cos{\left(3 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - \cos{\left(3 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(1 - \cos{\left(3 x \right)}\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(1 - \cos{\left(3 x \right)}\right) = 1 - \cos{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - \cos{\left(3 x \right)}\right) = 1 - \cos{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - \cos{\left(3 x \right)}\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(1 - \cos{\left(3 x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(1 - \cos{\left(3 x \right)}\right) = \left\langle 0, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 1^-}\left(1 - \cos{\left(3 x \right)}\right) = 1 - \cos{\left(3 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(1 - \cos{\left(3 x \right)}\right) = 1 - \cos{\left(3 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(1 - \cos{\left(3 x \right)}\right) = \left\langle 0, 2\right\rangle$$
More at x→-oo
One‐sided limits
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lim (1 - cos(3*x)) x->0+
$$\lim_{x \to 0^+}\left(1 - \cos{\left(3 x \right)}\right)$$
0
$$0$$
= -4.75153373652435e-31
lim (1 - cos(3*x)) x->0-
$$\lim_{x \to 0^-}\left(1 - \cos{\left(3 x \right)}\right)$$
0
$$0$$
= -4.75153373652435e-31
= -4.75153373652435e-31
The graph