Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-64+4^x)/(-3+x)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
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Limit of (-2+2*x^3+7*x)/(-4-x+3*x^3)
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Limit of (1-sin(x))/cos(x)
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Identical expressions
- (one - four *x)^(one -x)/x
- (1 minus 4 multiply by x) to the power of (1 minus x) divide by x
- (one minus four multiply by x) to the power of (one minus x) divide by x
- (1-4*x)(1-x)/x
- 1-4*x1-x/x
- (1-4x)^(1-x)/x
- (1-4x)(1-x)/x
- 1-4x1-x/x
- 1-4x^1-x/x
- (1-4*x)^(1-x) divide by x
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Similar expressions
- (1+4*x)^(1-x)/x
- (1-4*x)^(1+x)/x
Limit of the function (1-4*x)^(1-x)/x
The solution
You have entered
[src]
/ 1 - x\
|(1 - 4*x) |
lim |--------------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right)$$
Limit((1 - 4*x)^(1 - x)/x, x, 0)
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
$$\lim_{x \to 0^-}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right) = -\infty$$
More at x→-oo
One‐sided limits
[src]
/ 1 - x\
|(1 - 4*x) |
lim |--------------|
x->0+\ x /
$$\lim_{x \to 0^+}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right)$$
oo
$$\infty$$
= 147.026138388191
/ 1 - x\
|(1 - 4*x) |
lim |--------------|
x->0-\ x /
$$\lim_{x \to 0^-}\left(\frac{\left(1 - 4 x\right)^{1 - x}}{x}\right)$$
-oo
$$-\infty$$
= -155.026840193896
= -155.026840193896
The graph