Question

Consider the following function.f(x) = 6x^2 − 4xFind the limit.

Answer 1

Given:-

`f(x)=6x^2-4x`

To find:-

`\lim _(\Delta x\to0)(f(x+\Delta x)-f(x))/(\Delta x)_{}`

So now we substitute the known values we get,

`(f(x+\Delta x)-f(x))/(\Delta x)_{}=(6(x+\Delta x)^2-6x^2+4x)/(\Delta x)`

So by furthur simplification. we get,

`(6(x+\Delta x)^2-6x^2+4x)/(\Delta x)=(6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x)/(\Delta x)`

So we get is,

`(6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x)/(\Delta x)=\frac{12x\Delta x+(\Delta x)^2^{}+4x}{\Delta x}`

So by furthur simplification we get,