Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-2+x)/(1+x))^(-3+2*x)
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Limit of (-2*asin(x)+asin(2*x))/x^3
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Limit of (1/x)^(1/x)
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Limit of (-2-3*x+2*x^2)/(2+x^2-3*x)
- Derivative of:
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cos(2*x)
- Graphing y =:
- cos(2*x)
- Integral of d{x}:
- cos(2*x)
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Identical expressions
- cos(two *x)
- co sinus of e of (2 multiply by x)
- co sinus of e of (two multiply by x)
- cos(2x)
- cos2x
Limit of the function cos(2*x)
The solution
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lim cos(2*x) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+} \cos{\left(2 x \right)}$$
Limit(cos(2*x), x, pi/2)
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
$$\lim_{x \to \frac{\pi}{2}^-} \cos{\left(2 x \right)} = -1$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+} \cos{\left(2 x \right)} = -1$$
$$\lim_{x \to \infty} \cos{\left(2 x \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \cos{\left(2 x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(2 x \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(2 x \right)} = \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(2 x \right)} = \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(2 x \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+} \cos{\left(2 x \right)} = -1$$
$$\lim_{x \to \infty} \cos{\left(2 x \right)} = \left\langle -1, 1\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-} \cos{\left(2 x \right)} = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cos{\left(2 x \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cos{\left(2 x \right)} = \cos{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cos{\left(2 x \right)} = \cos{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cos{\left(2 x \right)} = \left\langle -1, 1\right\rangle$$
More at x→-oo
One‐sided limits
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lim cos(2*x) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+} \cos{\left(2 x \right)}$$
-1
$$-1$$
= -1.0
lim cos(2*x) pi x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-} \cos{\left(2 x \right)}$$
-1
$$-1$$
= -1.0
= -1.0
The graph