Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-2+x)/x)^(2*x)
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Limit of (1+x)^(3/2)/(2+x)^(3/2)
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Limit of (1/4+1/x)/(4+x)
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Limit of (-exp(-sin(2*x))+exp(tan(2*x)))/(-1+sin(x))
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Identical expressions
- (one / four + one /x)/(four +x)
- (1 divide by 4 plus 1 divide by x) divide by (4 plus x)
- (one divide by four plus one divide by x) divide by (four plus x)
- 1/4+1/x/4+x
- (1 divide by 4+1 divide by x) divide by (4+x)
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Similar expressions
- (1/4+1/x)/(4-x)
- (1/4-1/x)/(4+x)
Limit of the function (1/4+1/x)/(4+x)
The solution
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[src]
/1 1\
|- + -|
|4 x|
lim |-----|
x->-4+\4 + x/
$$\lim_{x \to -4^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right)$$
Limit((1/4 + 1/x)/(4 + x), x, -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]
/1 1\
|- + -|
|4 x|
lim |-----|
x->-4+\4 + x/
$$\lim_{x \to -4^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right)$$
-1/16
$$- \frac{1}{16}$$
= -0.0625
/1 1\
|- + -|
|4 x|
lim |-----|
x->-4-\4 + x/
$$\lim_{x \to -4^-}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right)$$
-1/16
$$- \frac{1}{16}$$
= -0.0625
= -0.0625
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -4^-}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = - \frac{1}{16}$$
More at x→-4 from the left
$$\lim_{x \to -4^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = - \frac{1}{16}$$
$$\lim_{x \to \infty}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = 0$$
More at x→-oo
More at x→-4 from the left
$$\lim_{x \to -4^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = - \frac{1}{16}$$
$$\lim_{x \to \infty}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = \frac{1}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = \frac{1}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\frac{1}{4} + \frac{1}{x}}{x + 4}\right) = 0$$
More at x→-oo
The graph