Question

Find the limit as h goes to 0 of the quotient of the quantity 5 times the square of the quantity x plus h, minus 2 minus the quantity 5 times x squared minus 2, and h.
5x^2 + h^2 + 7

10x

3x^2 – 2

10x – 2

Answer 1

Expand
$\lim_{h \to 0} \frac{5(x^2+2hx+h^2)-2)-5x^2+2}{h}$

$\lim_{h \to 0} \frac{5x^2+10hx+5h^2-2-5x^2+2}{h}$

$\lim_{h \to 0} \frac{10hx+5h^2}{h}$

$\lim_{h \to 0} 10x+5h$
say h=0 so
10x

answer is 2nd one