OBLICZANIE GRANIC

[mtworek98]

Oblicz granicę.

\(a) \Lim_{x\to 16}\frac{x-16}{\sqrt{x}-4}\)
\(b) \Lim_{x\to 3}\frac{\sqrt{x}-\sqrt{3}}{x-3}\)
\(d) \Lim_{x\to -1}\frac{\sqrt{2+x}-1}{x+1}\)
\(e) \Lim_{x\to \frac{1}{2}}\frac{\sqrt{4x-1}-1}{2x-1}\)

[eresh]

Oblicz granicę.

\(a) \Lim_{x\to 16}\frac{x-16}{\sqrt{x}-4}\)

\(\Lim_{x\to 16}\frac{(\sqrt{x}-4)(\sqrt{x}+4)}{\sqrt{x}-4}=\Lim_{x\to 16}(\sqrt{x}+4)=4+4=8\)

[eresh]

Oblicz granicę.

\(b) \Lim_{x\to 3}\frac{\sqrt{x}-\sqrt{3}}{x-3}\)

\(\Lim_{x\to 3}\frac{\sqrt{x}-\sqrt{3}}{(\sqrt{x}-\sqrt{3})(\sqrt{x}+\sqrt{3})}=\Lim_{x\to 3}\frac{1}{\sqrt{x}+\sqrt{3}}=\frac{1}{2\sqrt{3}}\)

[eresh]

Oblicz granicę.

\(d) \Lim_{x\to -1}\frac{\sqrt{2+x}-1}{x+1}\)

\(\Lim_{x\to -1}\frac{(\sqrt{2+x}-1)(\sqrt{2+x}+1)}{(x+1)(\sqrt{2+x}+1)}=\Lim_{x\to -1}\frac{2+x-1}{(x+1)(\sqrt{2+x}+1)}=\Lim_{x\to -1}\frac{1}{\sqrt{2+x}+1}=\frac{1}{2}\)

[eresh]

Oblicz granicę.

\(e) \Lim_{x\to \frac{1}{2}}\frac{\sqrt{4x-1}-1}{2x-1}\)

\(\Lim_{x\to \frac{1}{2}}\frac{(\sqrt{4x-1}-1)(\sqrt{4x-1}+1)}{(2x-1)(\sqrt{4x-1}+1)}=\Lim_{x\to \frac{1}{2}}\frac{4x-1-1}{(2x-1)(\sqrt{4x-1}+1)}=\Lim_{x\to \frac{1}{2}}\frac{1}{\sqrt{4x-1}+1}=\frac{1}{2}\)