Mister Exam
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- Limit of the function:
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Limit of (-1+sqrt(6-x))/(2-sqrt(-1+x))
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Limit of (x+tan(x))*sin(x)
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Limit of (-2*sin(2*x)+sin(4*x))/(x*log(cos(6*x)))
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Limit of sin(3*x)^2-sin(x)^2/x^2
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Identical expressions
- (x+tan(x))*sin(x)
- (x plus tangent of (x)) multiply by sinus of (x)
- (x+tan(x))sin(x)
- x+tanxsinx
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Similar expressions
- (-sin(x)+tan(x))*sin(x)/x
- (x-tan(x))*sin(x)
- (-sin(x)+tan(x))*sin(x)/x^2
- (x+tan(x))*sinx
Limit of the function (x+tan(x))*sin(x)
The solution
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[src]
lim ((x + tan(x))*sin(x)) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
Limit((x + tan(x))*sin(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 ((x + tan(x))*sin(x)) pi x->--+ 2
$$\lim_{x \to \frac{\pi}{2}^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
-oo
$$-\infty$$
= -149.417097037783836292768495866475810238931983763004365753348275676538876324
lim ((x + tan(x))*sin(x)) pi x->--- 2
$$\lim_{x \to \frac{\pi}{2}^-}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
oo
$$\infty$$
= 152.558620800068444969848837760312316847393942100166014632297394053007337313
= 152.558620800068444969848837760312316847393942100166014632297394053007337313
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{2}^-}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = -\infty$$
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = \sin{\left(1 \right)} + \sin{\left(1 \right)} \tan{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = \sin{\left(1 \right)} + \sin{\left(1 \right)} \tan{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
More at x→-oo
More at x→pi/2 from the left
$$\lim_{x \to \frac{\pi}{2}^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = \sin{\left(1 \right)} + \sin{\left(1 \right)} \tan{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right) = \sin{\left(1 \right)} + \sin{\left(1 \right)} \tan{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(x + \tan{\left(x \right)}\right) \sin{\left(x \right)}\right)$$
More at x→-oo
Numerical answer
[src]
-149.417097037783836292768495866475810238931983763004365753348275676538876324
-149.417097037783836292768495866475810238931983763004365753348275676538876324
The graph