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

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 Solution

 Formulas

 Videos

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Calculus - How to find the limit of continuous functions, lim(x tends to -3) (x^2 - 8)

https://www.youtube.com/watch?v=RbT5vQajMio

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

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

Pre-Calculus - Operations with functions, f(x) = x^2 +3 ,g(x) = 2x-1

https://www.youtube.com/watch?v=WZTqq4K8dCA

Pre-Calculus - Operations with functions f(x) = 2x -5 , g(x) = 2-x and f(x) = x^2+6 , g(x) root(1-x)

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

Power Series Representation With Natural Logarithms - Calculus 2

https://www.youtube.com/watch?v=A6JdlY52NFg

 Function Plot

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

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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).

 Used Formulas

See formulas (10)

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