Question

Find the limit of f(x)= 3x^2 c=1 if lim x approaches c f(x)- f(c)/x-c

Answer 1

F(x) = 3x², c = 1

$\lim_{x\to c}\frac{f(x) - f(c)}{x - c}$
$\lim_{x\to c}\frac{3x^{2} - 3c^{2}}{x - c}$
$\lim_{x\to c}\frac{3x^{2} - 3}{x - 1}$
$\lim_{x\to c}\frac{3(x^{2} - 1)}{x - 1}$
$\lim_{x\to c}\frac{3(x - 1)(x + 1)}{x - 1}$
$\lim_{x\to c}3(x + 1)$
$\lim_{x\to c}3x + 3$
$3c + 3$
$3(1) + 3$
$3 + 3$
$6$