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

Question

asked Apr 3, 2023 172k views

1 Answer

Remy Blank · Answer 1 · 2023-04-08T16:45:43+0000

Given:-

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,