Question

Please Help! It is Pre-Calc and I need to know the answer!

Answer 1

That's the derivative at 2 so is going to be 2(2)+1=5, second choice, but let's do it the hard way.

`\displaystyle \lim_(h \to 0) (f(2+h)-f(2))/(h) = \lim_(h \to 0) ((2+h)^2 + (2+h) + 1 -(2^2 + 2 + 1))/(h)`

`\displaystyle =\lim_(h \to 0) (4 + 4h +h^2 +h-4)/(h)=\lim_(h \to 0) (h^2 +5h)/(h) = \lim_(h \to 0) h+5 = 5`

Answer: 5, second choice