Question

h tende a 0 lim 4- V(16+h)/h

Answer 1

$\lim_{h \to 0} \frac{4- \sqrt{16+h} }{h} = \\ = \lim_{h \to 0} \frac{4- \sqrt{16+h} }{h} \frac{4+ \sqrt{16+h} }{4+ \sqrt{16+h} } \\ = \lim_{h \to 0} \frac{16-(16+h)}{h( 4+\sqrt{16+h)} } \\ = \lim_{h \to 0} \frac{16-16-h}{h(4+ \sqrt{16+h}) } \\ = \lim_{h \to 0} \frac{-h}{h (4+\sqrt{16+h}) } \\ = \lim_{h \to 0} \frac{-1}{ 4+\sqrt{16+h} } \\ = \frac{-1}{ 4+\sqrt{16} } = \frac{-1}{8}$