👉 Try now NerdPal! Our new math app on iOS and Android
  1. calculators
  2. Limits

Limits Calculator

Get detailed solutions to your math problems with our Limits step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Here, we show you a step-by-step solved example of limits. This solution was automatically generated by our smart calculator:

$\lim_{x\to4}\left(\frac{x-4}{\sqrt{x}-2}\right)$

The value of $a$ is $\sqrt{x}$.

and the value of $b$ is $-2$, therefore:

The fraction $\frac{x-4}{\sqrt{x}-2}$ simplified equals $\sqrt{x}+2$.

2

The difference of the squares of two terms, divided by the sum of the same terms, is equal to the difference of the terms. In other words: $\displaystyle\frac{a^2-b^2}{a+b}=a-b$.

$\lim_{x\to4}\left(\sqrt{x}+2\right)$
3

Evaluate the limit $\lim_{x\to4}\left(\sqrt{x}+2\right)$ by replacing all occurrences of $x$ by $4$

$\sqrt{4}+2$
4

Calculate the power $\sqrt{4}$

$2+2$
5

Add the values $2$ and $2$

$4$

Final answer to the problem

$4$

Are you struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!