Question

If $f\left(x\right)=3x^2-7x+5$, then $\underset{x\to 0}{lim}\frac{f\left(x\right)-f\left(0\right)}{x}$ is equal to

• A. $6$
• B. $-7$
• C. $7$
• D. $-6$
• E. $5$

Answer 1

Answer: (B)

$-7$

Given, $f\left(x\right)=3x^2-7x+5$

$\underset{x\to 0}{lim}\frac{f\left(x\right)-f\left(0\right)}{x}$
$=\underset{x\to 0}{lim}\frac{(3x^2-7x+5)-\left(5\right)}{x}$
$=\underset{x\to 0}{lim}\frac{3x^2-7x}{x}$
$=\underset{x\to 0}{lim}3x-7=-7$