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Find the limit of $\left(\frac{3x^2-x+1}{2x^2+x+1}\right)^{\frac{x^3}{1-x}}$ as $x$ approaches 0

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 Solution

 Videos

_-substitution: definite integral of exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=1ct7LUx23io

Limit of (sin x)/x as x approaches 0

https://www.youtube.com/watch?v=5xitzTutKqM

Finding specific antiderivatives: exponential function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=T8rbpI4OZCc

If function u is continuous at x, then _u_0 as _x_0 | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=l6T4RhlgkG0

Algebra 2 - Determine and describe the discriminant 5x^2 - x -1 = 0

https://www.youtube.com/watch?v=F3eTBxCnzvI

Calculus - Evaluating a limit by rationalizing the radical, lim(x tends to 0) (sqrt(x + 1) - 1)/x

https://www.youtube.com/watch?v=v8dIvXm03dw

 Function Plot

Plotting: $\left(\frac{3x^2-x+1}{2x^2+x+1}\right)^{\frac{x^3}{1-x}}$

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Got a different answer? Verify it!

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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

D^□_x

∫

∫^◻

|◻|

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

 How to improve your answer:

 Main Topic: Limits of Exponential Functions

Those are limits of expressions of the form f(x)^g(x).

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