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Selamat datang di halaman contoh soal dan pembahasan "Limit".
Di halaman ini akan membahas tentang contoh soal dan pembahasan lengkap mengenai Limit.
Untuk lebih jelasnya mari kita lihat contoh soal dan pembahasan dibawah ini!
a.17 b.18 c.21 d.19 e.20
Pembahasan:
\(\lim\limits_{x\rightarrow 2}3x^{2}+5=3(2)^{2}+5=3(4)+5=17\)
\(2.\lim\limits_{x\rightarrow 2}\frac{x^{2}+5x+6}{x^{2}-4}=...\)
\(a.\frac{1}{4}\)
\(b.-\frac{1}{4}\)
\(c.\frac{1}{2}\)
\(d.-\frac{1}{2}\)
\(e.1\)
Pembahasan:
\(\lim\limits_{x\rightarrow 2}\frac{x^{2}-5x+6}{x^{2}-4}=\lim\limits_{x\rightarrow 2}\frac{2x-5}{2x}=\frac{2(2)-5}{2(2)}=\frac{4-5}{4}=\frac{-1}{4}\)
\(3. \lim\limits_{x\rightarrow 2}\frac{x^{2}-16}{x-4}=...\)
a. 2 b. 4 c. 6 d. -4 e. -2
Pembahasan:
\(\lim\limits_{x\rightarrow 2}\frac{x^{2}-16}{x-4}=\lim\limits_{x\rightarrow 2}\frac{(x-4)(x+4)}{(x-4)}=\lim\limits_{x\rightarrow 2}x+4=2+4=6\)
\(4. \lim\limits_{x\rightarrow 3}\frac{x^{2}+2x-15}{x-3}=...\)
a. 5 b. -2 c. 0 d. 3 e. 8
Pembahasan:
\(\lim\limits_{x\rightarrow 3}\frac{x^{2}+2x-15}{x-3}=\lim\limits_{x\rightarrow 3}\frac{(x-3)(x+5)}{(x-3)}=\lim\limits_{x\rightarrow 3}x+5=3+5=8\)
\(5. \lim\limits_{x\rightarrow 0}{x^{2}-3x+2}=... \)
a.-2 b. 2 c. 3 d. 0 e. -3
Pembahasan:
\(\lim\limits_{x\rightarrow 0}{x^{2}-3x+2}=(0)^{2}-3(0)+2=2\)
\(6. \lim\limits_{x\rightarrow 4}\frac{x^{2}-4}{x-2}= \)
a.4 b.6 c.2 d.8 e.0
Pembahasan
\(\lim\limits_{x\rightarrow 4}\frac{x^{2}-4}{x-2}=\lim\limits_{x\rightarrow 4}\frac{(x-2)(x+2)}{(x-2)}=\lim\limits_{x\rightarrow 4}x+2=4+2=6\)
\(7. \lim\limits_{x\rightarrow 2}\frac{x^{3}-8}{x+2}=... \)
a.2 b.-2 c.0 d.6 e.-6
Pembahasan:
\(\lim\limits_{x\rightarrow 2}\frac{x^{3}-8}{x+2}=\frac{2^{3}-8}{2+2}=\frac{0}{4}=0\)
\(8. \lim\limits_{x\rightarrow 4}\frac{3x^{3}-48x}{x^{2}-16}=... \)
a.8 b.14 c.12 d.16 e.6
Pembahasan:
\(\lim\limits_{x\rightarrow 4}\frac{3x^{3}-48x}{x^{2}-16}=\lim\limits_{x\rightarrow 4}\frac{3x(x^{2}-16)}{(x^{2}-16)}=\lim\limits_{x\rightarrow 4}3x=3(4)=12\)
\(9. \lim\limits_{x\rightarrow 3}\frac{x^{2}-9}{x^{3}-27}=... \)
\(a.\frac{1}{2}\) \(b.\frac{2}{9}\) \(c.\frac{4}{9}\) \(d.\frac{1}{3} e.1\)
Pembahasan:
\(\lim\limits_{x\rightarrow 3}\frac{x^{2}-9}{x^{3}-27}\)
\(=\lim\limits_{x\rightarrow 3}\frac{(x-3)(x+3)}{(x-3)(x^{2}+3x+9)}\)
\(=\lim\limits_{x\rightarrow 3}\frac{x+3}{x^{2}+3x+9}\)
\(=\frac{3+3}{3^{2}+3(3)+9}\)
\(=\frac{6}{27}\)
\(=\frac{2}{9}\)
\(10. \lim\limits_{x\rightarrow 2}\frac{x^{2}-2x-3}{x^{2}-9}=... \)
\(a.\frac{2}{7}\) \(b.\frac{3}{7}\) \(c.\frac{5}{7}\) \(d.\frac{9}{7} \) e.\frac{1}{7}\)
Pembahasan:
\(\lim\limits_{x\rightarrow 3}\frac{x^{2}-2x-3}{x^{2}-9}\)
\(=\lim\limits_{x\rightarrow 3}\frac{(x-3)(x+1)}{(x-3)(x+3)}\)
\(=\lim\limits_{x\rightarrow 3}\frac{x+1}{x+3}\)
\(=\frac{3+1}{3+3}\)
\(=\frac{4}{6}\)
\(=\frac{2}{3}\)
