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Find the limit of $\frac{\sqrt{4x^2-2}}{1-x}$ as $x$ approaches $\infty $

Step-by-step Solution

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Final Answer

$-2$
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Step-by-step Solution

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As it's an indeterminate limit of type $\frac{\infty}{\infty}$, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is $x$

$\lim_{x\to\infty }\left(\frac{\frac{\sqrt{4x^2-2}}{x}}{\frac{1-x}{x}}\right)$

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(\frac{\frac{\sqrt{4x^2-2}}{x}}{\frac{1-x}{x}}\right)$

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Learn how to solve limits to infinity problems step by step online. Find the limit of ((4x^2-2)^1/2)/(1-x) as x approaches infinity. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is x. Rewrite the fraction, in such a way that both numerator and denominator are inside the exponent or radical. Separate the terms of both fractions. Simplify the fraction \frac{-x}{x} by x.

Final Answer

$-2$

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Function Plot

Plotting: $\frac{\sqrt{4x^2-2}}{1-x}$

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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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Main Topic: Limits to Infinity

The limit of a function f(x) when x tends to infinity is the value that the function takes as the value of x grows indefinitely.

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