Question

Help Please ASAP!!!!!!!

Answer 1

`4x`

Explanation:

Step 1: Define

I will substitute delta x with h

`\lim_(h \to 0) (2(x+h)^2-2x^2)/(h)`

Step 2: Simplify function

1. Expand:
   `\lim_(h \to 0) (2(x^2+2hx+h^2)-2x^2)/(h)`
2. Distribute 2:
   `\lim_(h \to 0) (2x^2+4hx+2h^2-2x^2)/(h)`
3. Combine like terms:
   `\lim_(h \to 0) (4hx+2h^2)/(h)`
4. Factor:
   `\lim_(h \to 0) (h(4x+2h))/(h)`
5. Simplify:
   `\lim_(h \to 0) 4x+2h`

Step 3: Evaluate limit

`\lim_(h \to 0) 4x+2h=\lim_(h \to 0) 4x+2(0)`

`\lim_(h \to 0) 4x+2(0)=\lim_(h \to 0) 4x+0`

`\lim_(h \to 0) 4x+0 = 4x`