Given the funtion G(t) = t2 - 7t + 5, evaluate G(-1+h)-G(-1)/h
g(-1+h) = (-1+h)^2 - 7(-1+h) + 5
= 1 - 2h + h^2 + 7 - 7h + 5
= h^2 - 9h + 13
g(-1) = 1 + 7 + 5 = 13
( g(-1+h) - g(-1) )/h = (h^2 - 9h + 13 - 13)/h
= h - 9
To evaluate the given expression, G(-1+h) - G(-1)/h, we need to substitute the values of G(-1+h) and G(-1) into the expression and simplify it.
First, let's find the value of G(-1+h):
G(t) = t^2 - 7t + 5
Replace t with (-1+h):
G(-1+h) = (-1+h)^2 - 7(-1+h) + 5
Expanding the square:
G(-1+h) = (1 - 2h + h^2) + 7 - 7h + 5
Simplifying:
G(-1+h) = h^2 - 9h + 13
Now, let's find the value of G(-1):
G(t) = t^2 - 7t + 5
Replace t with -1:
G(-1) = (-1)^2 - 7(-1) + 5
Simplifying:
G(-1) = 1 + 7 + 5 = 13
Now, substitute these values into the expression G(-1+h) - G(-1)/h:
(h^2 - 9h + 13 - 13) / h
Simplifying:
(h^2 - 9h) / h
Finally, the expression simplifies to:
h^2 - 9h / h
Therefore, the simplified expression is h - 9.