Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of -2+x^3+6*x
-
Limit of 1+sqrt(x)-3/x
-
Limit of (-3+sqrt(1+4*x))/(-2+x)
-
Limit of log(1+sin(2*x))/tan(5*x)
-
Identical expressions
- one +sqrt(x)- three /x
- 1 plus square root of (x) minus 3 divide by x
- one plus square root of (x) minus three divide by x
- 1+√(x)-3/x
- 1+sqrtx-3/x
- 1+sqrt(x)-3 divide by x
-
Similar expressions
- 1-sqrt(x)-3/x
- 1+sqrt(x)+3/x
Limit of the function 1+sqrt(x)-3/x
The solution
You have entered
[src]
/ ___ 3\ lim |1 + \/ x - -| x->4+\ x/
$$\lim_{x \to 4^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right)$$
Limit(1 + sqrt(x) - 3/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]
/ ___ 3\ lim |1 + \/ x - -| x->4+\ x/
$$\lim_{x \to 4^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right)$$
9/4
$$\frac{9}{4}$$
= 2.25
/ ___ 3\ lim |1 + \/ x - -| x->4-\ x/
$$\lim_{x \to 4^-}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right)$$
9/4
$$\frac{9}{4}$$
= 2.25
= 2.25
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 4^-}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \frac{9}{4}$$
More at x→4 from the left
$$\lim_{x \to 4^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \frac{9}{4}$$
$$\lim_{x \to \infty}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \infty i$$
More at x→-oo
More at x→4 from the left
$$\lim_{x \to 4^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \frac{9}{4}$$
$$\lim_{x \to \infty}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = -1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = -1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(\sqrt{x} + 1\right) - \frac{3}{x}\right) = \infty i$$
More at x→-oo
The graph