If limit of f(x)=27 as x rightarrow c, what the limit of (f(x))^2 as x rightarrow c?

Afzal2wl

Afzal2wl

Answered question

2023-02-10

How to solve lim x a f ( x ) g ( a ) - f ( a ) g ( x ) x - a , if f, g have derivative on x = a ?

Answer & Explanation

Ivan Barrett

Ivan Barrett

Beginner2023-02-11Added 6 answers

Step 1
f ( x ) g ( a ) - f ( a ) g ( x ) x - a = f ( x ) g ( x ) - f ( a ) g ( x ) - ( f ( x ) g ( x ) - f ( x ) g ( a ) ) x - a =
( f ( x ) - f ( a ) ) g ( x ) x - a - ( g ( x ) - g ( a ) ) f ( x ) x - a
Step 2
Therefore,
lim x a f ( x ) g ( a ) - f ( a ) g ( x ) x - a = f ( a ) g ( a ) - g ( a ) f ( a )

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