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Find the limit (Picture Provided)

Find the limit (Picture Provided)-example-1
User Artagnon
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ANSWER


a. \: 4

Step-by-step explanation

Given:


f(x) = {x}^(2)


f(2) = 4


f(2 + h) = {(2 + h)}^(2)


f(2 + h) = {h}^(2) + 4h + 4


lim_(h\to 0) (f(x + h) - f(2))/(h)

Substitute;


lim_(h\to 0) \frac{ {h}^(2) + 4h + 4 - 4}{h}


lim_(h\to 0) \frac{ {h}^(2) + 4h }{h}


lim_(h\to 0) h + 4

Plug in zero,


= 0 + 4


= 4

User Kopiczko
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