6. ) let f(x)=x^2,evalute f(h-2)-f(-2)/h
H->0
7.) evalute lim-2x^2+x/x
x->0
To evaluate these expressions, we will start by simplifying them and then substitute the given values.
For question 6:
Step 1: Simplify the expression f(h-2)-f(-2)/h
Substitute the function f(x) = x^2 into the expression:
f(h-2) = (h-2)^2
f(-2) = (-2)^2 = 4
The expression becomes ((h-2)^2 - 4)/h
Step 2: Evaluate the expression as h approaches 0 (H->0)
Substitute h=0 into the expression:
((0-2)^2 - 4)/0 = ((-2)^2 - 4)/0 = (4 - 4)/0 = 0/0
This expression is undefined since we have an indeterminate form of 0/0.
Therefore, the expression f(h-2)-f(-2)/h, as h approaches 0, is undefined.
For question 7:
Step 1: Simplify the expression -2x^2 + x/x
Simplify the expression by factoring out x:
-2x^2 + x/x = -2x + 1
Step 2: Evaluate the expression as x approaches 0 (x->0)
Substitute x=0 into the expression:
-2(0) + 1 = 0 + 1 = 1
Therefore, the expression -2x^2 + x/x, as x approaches 0, evaluates to 1.