Mister Exam
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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 -cos(x)+5*x
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Limit of sin(5*x)/(4*x^2)
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Identical expressions
- - one +sqrt(five)-sqrt(two)- two *x
- minus 1 plus square root of (5) minus square root of (2) minus 2 multiply by x
- minus one plus square root of (five) minus square root of (two) minus two multiply by x
- -1+√(5)-√(2)-2*x
- -1+sqrt(5)-sqrt(2)-2x
- -1+sqrt5-sqrt2-2x
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Similar expressions
- -1+sqrt(5)-sqrt(2)+2*x
- -1+sqrt(5)+sqrt(2)-2*x
- 1+sqrt(5)-sqrt(2)-2*x
- -1-sqrt(5)-sqrt(2)-2*x
Limit of the function -1+sqrt(5)-sqrt(2)-2*x
The solution
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/ ___ ___ \ lim \-1 + \/ 5 - \/ 2 - 2*x/ x->1+
$$\lim_{x \to 1^+}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right)$$
Limit(-1 + sqrt(5) - sqrt(2) - 2*x, x, 1)
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 \-1 + \/ 5 - \/ 2 - 2*x/ x->1+
$$\lim_{x \to 1^+}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right)$$
___ ___ -3 + \/ 5 - \/ 2
$$-3 - \sqrt{2} + \sqrt{5}$$
= -2.17814558487331
/ ___ ___ \ lim \-1 + \/ 5 - \/ 2 - 2*x/ x->1-
$$\lim_{x \to 1^-}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right)$$
___ ___ -3 + \/ 5 - \/ 2
$$-3 - \sqrt{2} + \sqrt{5}$$
= -2.17814558487331
= -2.17814558487331
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = -3 - \sqrt{2} + \sqrt{5}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = -3 - \sqrt{2} + \sqrt{5}$$
$$\lim_{x \to \infty}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = - \sqrt{2} - 1 + \sqrt{5}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = - \sqrt{2} - 1 + \sqrt{5}$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = \infty$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = -3 - \sqrt{2} + \sqrt{5}$$
$$\lim_{x \to \infty}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = - \sqrt{2} - 1 + \sqrt{5}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = - \sqrt{2} - 1 + \sqrt{5}$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(- 2 x + \left(- \sqrt{2} + \left(-1 + \sqrt{5}\right)\right)\right) = \infty$$
More at x→-oo
The graph