construct a table and find the indicated limit. lim f(x), where f(x) = { x + 3 if x < 0; 3x + 3 if 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 } as x -> 0. complete the table below. 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 (simplify your answers. round to four decimal places as needed.) lim f(x) = (type an integer or a decimal.) as 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 } as x -> 0. complete the table below. 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 (simplify your answers. round to four decimal places as needed.) lim f(x) = (type an integer or a decimal.) as x -> 0

Answer

Explanation:

Step1: Analyze left - hand limit

For (x<0), (f(x)=x + 3). As (x) approaches (0) from the left ((x\to0^{-})), we substitute values from the left - hand side of the table into (f(x)=x + 3). As (x) gets closer to (0) from the left, (f(x)) gets closer to (0+3 = 3).

Step2: Analyze right - hand limit

For (x\geq0), (f(x)=3x + 3). As (x) approaches (0) from the right ((x\to0^{+})), we substitute values from the right - hand side of the table into (f(x)=3x + 3). As (x) gets closer to (0) from the right, (f(x)) gets closer to (3\times0+3=3).

Answer:

3