Mister Exam

Other calculators:

(-2+x)/(-4+x)
Limit of the function/ (-2+x)/(-4+x)

Limit of the function (-2+x)/(-4+x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /-2 + x\
 lim |------|
x->4+\-4 + x/
$$\lim_{x \to 4^+}\left(\frac{x - 2}{x - 4}\right)$$ 
Limit((-2 + 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
Plot the graph
One‐sided limits [src] 
     /-2 + x\
 lim |------|
x->4+\-4 + x/
$$\lim_{x \to 4^+}\left(\frac{x - 2}{x - 4}\right)$$ 
oo
$$\infty$$ 
= 303.0
     /-2 + x\
 lim |------|
x->4-\-4 + x/
$$\lim_{x \to 4^-}\left(\frac{x - 2}{x - 4}\right)$$ 
-oo
$$-\infty$$ 
= -301.0
= -301.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 4^-}\left(\frac{x - 2}{x - 4}\right) = \infty$$
More at x→4 from the left
$$\lim_{x \to 4^+}\left(\frac{x - 2}{x - 4}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{x - 2}{x - 4}\right) = 1$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x - 2}{x - 4}\right) = \frac{1}{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x - 2}{x - 4}\right) = \frac{1}{2}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x - 2}{x - 4}\right) = \frac{1}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x - 2}{x - 4}\right) = \frac{1}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x - 2}{x - 4}\right) = 1$$
More at x→-oo
Rapid solution [src] 
oo
$$\infty$$
Expand and simplify
Numerical answer [src] 
303.0
303.0
The graph
Limit of the function (-2+x)/(-4+x)
    © Mister Exam – Calculator