Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of e^(-x)*x^10
-
Limit of tan(7*x)/(3*x)
-
Limit of (sqrt(1+x)-sqrt(1-x))/(2*x)
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Limit of (4-4*e^(-x^2/2)+sin(x^2))/(x^3*(-1+e^x))
- Derivative of:
- 2*sin(x)/cos(x)
- Graphing y =:
- 2*sin(x)/cos(x)
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Identical expressions
- two *sin(x)/cos(x)
- 2 multiply by sinus of (x) divide by co sinus of e of (x)
- two multiply by sinus of (x) divide by co sinus of e of (x)
- 2sin(x)/cos(x)
- 2sinx/cosx
- 2*sin(x) divide by cos(x)
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Similar expressions
- (x-pi/2)*sin(x)/cos(x)
- 2*sinx/cosx
Limit of the function 2*sin(x)/cos(x)
The solution
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/2*sin(x)\ lim |--------| pi \ cos(x) / x->--+ 4
$$\lim_{x \to \frac{\pi}{4}^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
Limit((2*sin(x))/cos(x), x, pi/4)
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]
/2*sin(x)\ lim |--------| pi \ cos(x) / x->--+ 4
$$\lim_{x \to \frac{\pi}{4}^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
2
$$2$$
= 2.0
/2*sin(x)\ lim |--------| pi \ cos(x) / x->--- 4
$$\lim_{x \to \frac{\pi}{4}^-}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
2
$$2$$
= 2.0
= 2.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{4}^-}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 2$$
More at x→pi/4 from the left
$$\lim_{x \to \frac{\pi}{4}^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 2$$
$$\lim_{x \to \infty}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→-oo
More at x→pi/4 from the left
$$\lim_{x \to \frac{\pi}{4}^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 2$$
$$\lim_{x \to \infty}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}\right)$$
More at x→-oo
The graph