construct a table and find the indicated limit. lim f(x), where f(x)={x + 3 if x < 0; 3x + 3 if x >= 0} x→0…
construct a table and find the indicated limit. lim f(x), where f(x)={x + 3 if x < 0; 3x + 3 if x >= 0} x→0 complete the table below. x -0.01 -0.001 -0.0001 →← 0.0001 0.001 0.01 f(x) (simplify your answers. round to four decimal places as needed.)
Answer
Explanation:
Step1: Evaluate for $x < 0$ values
For $x=-0.01$, use $f(x)=x + 3$. So $f(-0.01)=-0.01+3=2.9900$. For $x=-0.001$, use $f(x)=x + 3$. So $f(-0.001)=-0.001+3=2.9990$. For $x=-0.0001$, use $f(x)=x + 3$. So $f(-0.0001)=-0.0001+3=2.9999$.
Step2: Evaluate for $x\geq0$ values
For $x = 0.0001$, use $f(x)=3x + 3$. So $f(0.0001)=3\times0.0001+3=3.0003$. For $x = 0.001$, use $f(x)=3x + 3$. So $f(0.001)=3\times0.001+3=3.0030$. For $x = 0.01$, use $f(x)=3x + 3$. So $f(0.01)=3\times0.01+3=3.0300$.
Answer:
| $x$ | $-0.01$ | $-0.001$ | $-0.0001$ | $0.0001$ | $0.001$ | $0.01$ |
|---|---|---|---|---|---|---|
| $f(x)$ | $2.9900$ | $2.9990$ | $2.9999$ | $3.0003$ | $3.0030$ | $3.0300$ |