Question

If a function f(x) is defined as 3x2 + x + 2, what is the value of Lim h-0 f(x+h)-f(x)/h? A. 3x + 1 B. 3x + 2 C. 6x + 1 D. 6x + 2

Answer 1

6x+1

Explanation:

Plato :)

Answer 2

`f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2`

`f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2`

And replacing we got:

`lim_(h \to 0) (3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2)/(h)`

And if we simplfy we got:

`lim_(h \to 0) (6xh +h+ 3h^2 )/(h) =lim_(h \to 0) 6x + 1 +3h`

And replacing we got:

`lim_(h \to 0) 6x + 1 +3h = 6x+1`

And the bet option would be:

C. 6x + 1

Explanation:

We have the following function given:

`f(x) = 3x^2 +x+2`

And we want to find this limit:

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

We can begin finding:

`f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2`

`f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2`

And replacing we got:

`lim_(h \to 0) (3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2)/(h)`

And if we simplfy we got:

`lim_(h \to 0) (6xh +h+ 3h^2 )/(h) =lim_(h \to 0) 6x + 1 +3h`

And replacing we got:

`lim_(h \to 0) 6x + 1 +3h = 6x+1`

And the bet option would be:

C. 6x + 1