Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
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Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
- Derivative of:
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-sin(x)+cos(x)
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Identical expressions
- -sin(x)+cos(x)
- minus sinus of (x) plus co sinus of e of (x)
- -sinx+cosx
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Similar expressions
- -sin(x)-cos(x)
- sin(x)+cos(x)
- -sinx+cosx
Limit of the function -sin(x)+cos(x)
The solution
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[src]
lim (-sin(x) + cos(x)) pi x->--+ 4
$$\lim_{x \to \frac{\pi}{4}^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
Limit(-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]
lim (-sin(x) + cos(x)) pi x->--+ 4
$$\lim_{x \to \frac{\pi}{4}^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
0
$$0$$
= 4.32978028117747e-17
lim (-sin(x) + cos(x)) pi x->--- 4
$$\lim_{x \to \frac{\pi}{4}^-}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)$$
0
$$0$$
= 4.32978028117746e-17
= 4.32978028117746e-17
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{4}^-}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 0$$
More at x→pi/4 from the left
$$\lim_{x \to \frac{\pi}{4}^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
More at x→pi/4 from the left
$$\lim_{x \to \frac{\pi}{4}^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 0$$
$$\lim_{x \to \infty}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→oo
$$\lim_{x \to 0^-}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = - \sin{\left(1 \right)} + \cos{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) = \left\langle -2, 2\right\rangle$$
More at x→-oo
The graph