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)
- Canonical form:
- sin(x)/cos(x)
- Integral of d{x}:
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sin(x)/cos(x)
- Derivative of:
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sin(x)/cos(x)
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Identical expressions
- sin(x)/cos(x)
- sinus of (x) divide by co sinus of e of (x)
- sinx/cosx
- sin(x) divide by cos(x)
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Similar expressions
- (-1+sin(x))/cos(x)
- (1-sin(x))/cos(x)
- (1-sin(x))/cos(x)^2
- (x-pi)*sin(x)/cos(x/2)^2
- sinx/cosx
Limit of the function sin(x)/cos(x)
The solution
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[src]
/sin(x)\ lim |------| pi \cos(x)/ x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
Limit(sin(x)/cos(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
[src]
/sin(x)\ lim |------| pi \cos(x)/ x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
-oo
$$-\infty$$
= -150.997792488028
/sin(x)\ lim |------| pi \cos(x)/ x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
oo
$$\infty$$
= 150.997792488025
= 150.997792488025
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = -\infty$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→-oo
The graph