Question

lim as x goes to 2 of (f(x))-f(2))/(x-2) when f(x)= 5x^2-x+1

Answer 1

19

Answer 2

what did you do? Did you plug in the equation for the top part and pug in 2 for f(2)?

Answer 3

f(x)-f(2)=5x^2-x+1-(5(2^2)-2+1)=5x^2-x+1-19
=5x^2-x-18=(x-2)(5x+9)
so thats whats on top so u have:
\[\frac{(x-2)(5x+9)}{x-2}\]

Answer 4

cancel then solve for x=2

Answer 5

numerator simplifies into (5x²-x-18), that can be factorized into (x-2)(5x+9),, simplify

Answer 6

the limit=18 by l'hopitals rule

Answer 7

it's 19

Answer 8

no, take the derivative of the numerator and the derivative of the denominator and then plug in 2. you get 18

Answer 9

by l'hopital's rule:\[\lim_{x \rightarrow 2} \frac{\frac{d}{dx}(f(x)-f(2)}{\frac{d}{dx}(x-2)}=\frac{f \prime(x)-0}{1-0}=f \prime (x)= f \prime (2)\]

Answer 10

the problem is basically asking for the slope at f(2). So to determine slopes, you calculate the first derivative at that point. Thus, the derivative, f'(x)=10x-2. So f'(2)=18

Answer 11

derivative= 10x-1
10*2-1=20-1=19

Answer 12

you are right, haha good call