Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-3+sqrt(1+4*x))/(-2+x)
-
Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
-
Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
-
Limit of (-1+x+6*x^2)/(1/2+x)
- Derivative of:
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(1+x)/(4-x^2)
- How do you in partial fractions?:
- (1+x)/(4-x^2)
-
Identical expressions
- (one +x)/(four -x^ two)
- (1 plus x) divide by (4 minus x squared )
- (one plus x) divide by (four minus x to the power of two)
- (1+x)/(4-x2)
- 1+x/4-x2
- (1+x)/(4-x²)
- (1+x)/(4-x to the power of 2)
- 1+x/4-x^2
- (1+x) divide by (4-x^2)
-
Similar expressions
- (1-x)/(4-x^2)
- (1+x)/(4+x^2)
Limit of the function (1+x)/(4-x^2)
The solution
You have entered
[src]
/1 + x \
lim |------|
x->2+| 2|
\4 - x /
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right)$$
Limit((1 + x)/(4 - x^2), x, 2)
Detail solution
Let's take the limit
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right)$$
transform
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right)$$
=
$$\lim_{x \to 2^+}\left(\frac{x + 1}{\left(-1\right) \left(x - 2\right) \left(x + 2\right)}\right)$$
=
$$\lim_{x \to 2^+}\left(- \frac{x + 1}{x^{2} - 4}\right) = $$
The final answer:
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right) = -\infty$$
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right)$$
transform
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right)$$
=
$$\lim_{x \to 2^+}\left(\frac{x + 1}{\left(-1\right) \left(x - 2\right) \left(x + 2\right)}\right)$$
=
$$\lim_{x \to 2^+}\left(- \frac{x + 1}{x^{2} - 4}\right) = $$
False
= -oo
The final answer:
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right) = -\infty$$
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]
/1 + x \
lim |------|
x->2+| 2|
\4 - x /
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right)$$
-oo
$$-\infty$$
= -113.312396694215
/1 + x \
lim |------|
x->2-| 2|
\4 - x /
$$\lim_{x \to 2^-}\left(\frac{x + 1}{4 - x^{2}}\right)$$
oo
$$\infty$$
= 113.187396351575
= 113.187396351575
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-}\left(\frac{x + 1}{4 - x^{2}}\right) = -\infty$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x + 1}{4 - x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{1}{4}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{1}{4}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{2}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{2}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x + 1}{4 - x^{2}}\right) = 0$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x + 1}{4 - x^{2}}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x + 1}{4 - x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{1}{4}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{1}{4}$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{2}{3}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x + 1}{4 - x^{2}}\right) = \frac{2}{3}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x + 1}{4 - x^{2}}\right) = 0$$
More at x→-oo
The graph