Let f(x) be the function 8x^2-5x+2 . Then the quotient [f(5+h)-(5)]/h
can be simplified to ah+b for:
a=
b=
i tried like 7 times stil getting it wrong.
a = -75
b = 82
To simplify the given expression, let's first calculate f(5+h):
f(x) = 8x^2 - 5x + 2
Substitute x = 5+h into the function:
f(5+h) = 8(5+h)^2 - 5(5+h) + 2
Expand and simplify:
f(5+h) = 8(25 + 10h + h^2) - 25 - 5h + 2
= 200 + 80h + 8h^2 - 25 - 5h + 2
= 177 + 75h + 8h^2
Now, use this expression to simplify the quotient [(f(5+h) - 5)]/h:
[(f(5+h) - 5)]/h = [(177 + 75h + 8h^2 - 5)]/h
= (177 + 75h + 8h^2 - 5)/h
= (8h^2 + 75h + 172)/h
Since there is a quadratic term (h^2) in the numerator, we cannot simplify this expression further by dividing both the numerator and the denominator by h. Therefore, a = 8 and b = 172.
Therefore, the simplified form of the quotient [(f(5+h) - 5)]/h is 8h + 172.
Now I just did one like this for you. You try.
f(5+h) = 8 (5+h)^2 -5(5+h) + 2
= 8(25 + 10 h +h^2) -25 -5h +2
= 200 + 80 h + 8 h^2 -23 -5h
= 8 h^2 + 75 h + 177
f(5) = 8(25) - 25 + 2 = 175+2
=177
difference = 8 h^2 + 75 h
divide by h
8 h + 75 answer
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check with calculus
df/dx = 16 x - 5
at x = 5
16*5 - 5 = 75 sure enough limit when h--> 0 :)