Find the limit of $\frac{\sqrt{1-x}-\sqrt{1+3x}}{x}$ as $x$ approaches 0

Step-by-step Solution

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Final answer to the problem

$-2$
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Step-by-step Solution

How should I solve this problem?

  • Solve using direct substitution
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Applying rationalisation

$\lim_{x\to0}\left(\frac{\sqrt{1-x}-\sqrt{1+3x}}{x}\frac{\sqrt{1-x}+\sqrt{1+3x}}{\sqrt{1-x}+\sqrt{1+3x}}\right)$

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$\lim_{x\to0}\left(\frac{\sqrt{1-x}-\sqrt{1+3x}}{x}\frac{\sqrt{1-x}+\sqrt{1+3x}}{\sqrt{1-x}+\sqrt{1+3x}}\right)$

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Learn how to solve problems step by step online. Find the limit of ((1-x)^(1/2)-(1+3x)^(1/2))/x as x approaches 0. Applying rationalisation. Multiply and simplify the expression within the limit. x+0=x, where x is any expression. Combining like terms -x and -3x.

Final answer to the problem

$-2$

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Function Plot

Plotting: $\frac{\sqrt{1-x}-\sqrt{1+3x}}{x}$

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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

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