Question

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

Answer 1

Given:-

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

To find:-

$\lim _{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}$

So now we substitute the known values we get,

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

So by furthur simplification. we get,

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

So we get is,

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

So by furthur simplification we get,

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