Find the limit of $\sqrt{x+2}-\sqrt{x}$ as $x$ approaches $\infty $

Step-by-step Solution

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

Final answer to the problem

0

Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.
1

Applying rationalisation

$\lim_{x\to\infty }\left(\left(\sqrt{x+2}-\sqrt{x}\right)\frac{\sqrt{x+2}+\sqrt{x}}{\sqrt{x+2}+\sqrt{x}}\right)$

Learn how to solve problems step by step online.

$\lim_{x\to\infty }\left(\left(\sqrt{x+2}-\sqrt{x}\right)\frac{\sqrt{x+2}+\sqrt{x}}{\sqrt{x+2}+\sqrt{x}}\right)$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution

Learn how to solve problems step by step online. Find the limit of (x+2)^(1/2)-x^(1/2) as x approaches infinity. Applying rationalisation. Multiply and simplify the expression within the limit. Cancel like terms x and -x. Evaluate the limit \lim_{x\to\infty }\left(\frac{2}{\sqrt{x+2}+\sqrt{x}}\right) by replacing all occurrences of x by \infty .

Final answer to the problem

0

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Help us improve with your feedback!

Function Plot

Plotting: $\sqrt{x+2}-\sqrt{x}$

Invest in your Education!

Help us make you learn faster

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.

Create an Account