Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
- Limit of ((-2+x+x^2)/(1+x^2))^(-5+2*x^2)
- Limit of (x+2*p)/p^2
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Limit of (20+x^2-9*x)/(-16+x^2)
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Limit of (-9+x^2)/(15+5*x)
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Identical expressions
- (x+ two *p)/p^ two
- (x plus 2 multiply by p) divide by p squared
- (x plus two multiply by p) divide by p to the power of two
- (x+2*p)/p2
- x+2*p/p2
- (x+2*p)/p²
- (x+2*p)/p to the power of 2
- (x+2p)/p^2
- (x+2p)/p2
- x+2p/p2
- x+2p/p^2
- (x+2*p) divide by p^2
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Similar expressions
- (x-2*p)/p^2
Limit of the function (x+2*p)/p^2
The solution
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[src]
/x + 2*p\
lim |-------|
x->p+| 2 |
\ p /
$$\lim_{x \to p^+}\left(\frac{2 p + x}{p^{2}}\right)$$
Limit((x + 2*p)/p^2, x, p)
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
One‐sided limits
[src]
/x + 2*p\
lim |-------|
x->p+| 2 |
\ p /
$$\lim_{x \to p^+}\left(\frac{2 p + x}{p^{2}}\right)$$
3 - p
$$\frac{3}{p}$$
/x + 2*p\
lim |-------|
x->p-| 2 |
\ p /
$$\lim_{x \to p^-}\left(\frac{2 p + x}{p^{2}}\right)$$
3 - p
$$\frac{3}{p}$$
3/p
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to p^-}\left(\frac{2 p + x}{p^{2}}\right) = \frac{3}{p}$$
More at x→p from the left
$$\lim_{x \to p^+}\left(\frac{2 p + x}{p^{2}}\right) = \frac{3}{p}$$
$$\lim_{x \to \infty}\left(\frac{2 p + x}{p^{2}}\right) = \infty \operatorname{sign}{\left(\frac{1}{p^{2}} \right)}$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2}{p}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2}{p}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2 p + 1}{p^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2 p + 1}{p^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2 p + x}{p^{2}}\right) = - \infty \operatorname{sign}{\left(\frac{1}{p^{2}} \right)}$$
More at x→-oo
More at x→p from the left
$$\lim_{x \to p^+}\left(\frac{2 p + x}{p^{2}}\right) = \frac{3}{p}$$
$$\lim_{x \to \infty}\left(\frac{2 p + x}{p^{2}}\right) = \infty \operatorname{sign}{\left(\frac{1}{p^{2}} \right)}$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2}{p}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2}{p}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2 p + 1}{p^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{2 p + x}{p^{2}}\right) = \frac{2 p + 1}{p^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{2 p + x}{p^{2}}\right) = - \infty \operatorname{sign}{\left(\frac{1}{p^{2}} \right)}$$
More at x→-oo