Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of -sin(x)+tan(x)
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Limit of cos(x)*tan(5*x)
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Limit of -1+sqrt(5)-sqrt(2)-2*x
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Limit of ((-1+4*x)/(3+4*x))^(2+3*x)
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Identical expressions
- cos(x)*tan(five *x)
- co sinus of e of (x) multiply by tangent of (5 multiply by x)
- co sinus of e of (x) multiply by tangent of (five multiply by x)
- cos(x)tan(5x)
- cosxtan5x
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Similar expressions
- cos(x)^tan(5*x)
- cosx*tan(5*x)
Limit of the function cos(x)*tan(5*x)
The solution
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[src]
lim (cos(x)*tan(5*x)) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right)$$
Limit(cos(x)*tan(5*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
One‐sided limits
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lim (cos(x)*tan(5*x)) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right)$$
1/5
$$\frac{1}{5}$$
= 0.2
lim (cos(x)*tan(5*x)) pi x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right)$$
1/5
$$\frac{1}{5}$$
= 0.2
= 0.2
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \frac{1}{5}$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \frac{1}{5}$$
$$\lim_{x \to \infty}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \cos{\left(1 \right)} \tan{\left(5 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \cos{\left(1 \right)} \tan{\left(5 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \frac{1}{5}$$
$$\lim_{x \to \infty}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \cos{\left(1 \right)} \tan{\left(5 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \cos{\left(1 \right)} \tan{\left(5 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\cos{\left(x \right)} \tan{\left(5 x \right)}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph