Mister Exam
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How to use it?
- Limit of the function:
-
Limit of (10+12*x)/x^3
- Limit of (1+2*x/3)^(3251035981008077*x/140737488355328)
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Limit of (1-1/(5*n))^(2*n)
- Limit of (10+x)^(1/x)
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Identical expressions
- (ten + twelve *x)/x^ three
- (10 plus 12 multiply by x) divide by x cubed
- (ten plus twelve multiply by x) divide by x to the power of three
- (10+12*x)/x3
- 10+12*x/x3
- (10+12*x)/x³
- (10+12*x)/x to the power of 3
- (10+12x)/x^3
- (10+12x)/x3
- 10+12x/x3
- 10+12x/x^3
- (10+12*x) divide by x^3
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Similar expressions
- (10-12*x)/x^3
Limit of the function (10+12*x)/x^3
The solution
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[src]
/10 + 12*x\
lim |---------|
x->0+| 3 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
Limit((10 + 12*x)/x^3, x, 0)
Detail solution
Let's take the limit
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \left(6 x + 5\right)}{x^{3}}\right) = $$
The final answer:
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right) = \infty$$
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
transform
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
=
$$\lim_{x \to 0^+}\left(\frac{2 \left(6 x + 5\right)}{x^{3}}\right) = $$
False
= oo
The final answer:
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right) = \infty$$
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]
/10 + 12*x\
lim |---------|
x->0+| 3 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right)$$
oo
$$\infty$$
= 34703122.0
/10 + 12*x\
lim |---------|
x->0-| 3 |
\ x /
$$\lim_{x \to 0^-}\left(\frac{12 x + 10}{x^{3}}\right)$$
-oo
$$-\infty$$
= -34155898.0
= -34155898.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{12 x + 10}{x^{3}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{12 x + 10}{x^{3}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{12 x + 10}{x^{3}}\right) = 22$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{12 x + 10}{x^{3}}\right) = 22$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{12 x + 10}{x^{3}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{12 x + 10}{x^{3}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{12 x + 10}{x^{3}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{12 x + 10}{x^{3}}\right) = 22$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{12 x + 10}{x^{3}}\right) = 22$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{12 x + 10}{x^{3}}\right) = 0$$
More at x→-oo
The graph