Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^(4/x)
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Limit of (-6+x^2-x)/(-4+x^2)
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Limit of (-6+x^2-x)/(-21+x+2*x^2)
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Limit of e^(3-x)*(-2+x)
- Derivative of:
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cos(x)/(1-sin(x))
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Identical expressions
- cos(x)/(one -sin(x))
- co sinus of e of (x) divide by (1 minus sinus of (x))
- co sinus of e of (x) divide by (one minus sinus of (x))
- cosx/1-sinx
- cos(x) divide by (1-sin(x))
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Similar expressions
- (1+cos(x))/(1-sin(x))
- cos(x)/(1+sin(x))
- cos(x)/((1-sin(x))^2)^(1/3)
- cosx/(1-sinx)
Limit of the function cos(x)/(1-sin(x))
The solution
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/ cos(x) \ lim |----------| x->oo\1 - sin(x)/
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right)$$
Limit(cos(x)/(1 - sin(x)), x, oo, dir='-')
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \left\langle -\infty, \infty\right\rangle$$
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \frac{\cos{\left(1 \right)}}{- \sin{\left(1 \right)} + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \frac{\cos{\left(1 \right)}}{- \sin{\left(1 \right)} + 1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \frac{\cos{\left(1 \right)}}{- \sin{\left(1 \right)} + 1}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \frac{\cos{\left(1 \right)}}{- \sin{\left(1 \right)} + 1}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)}}{- \sin{\left(x \right)} + 1}\right) = \left\langle -\infty, \infty\right\rangle$$
More at x→-oo
The graph