Question

For $f(x) = \begin{cases} |x| & \text{if } x \le 0 \\ \sqrt{x} + 2 & \text{if } x > 0 \end{cases}$, find i. $\lim_{x \to 0^{-}} f(x) = $ ii. $\lim_{x \to 0^{+}} f(x) = $

          For $f(x) = \begin{cases} |x| & \text{if } x \le 0 \\ \sqrt{x} + 2 & \text{if } x > 0 \end{cases}$, find

i. $\lim_{x \to 0^{-}} f(x) = $

ii. $\lim_{x \to 0^{+}} f(x) = $

For f(x) = |x| if x ≤ 0
√(x) + 2 if x > 0, find

i. limx → 0^- f(x) =

ii. limx → 0^+ f(x) =

Added by Tom-S R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Lauren Shelton

08/17/2021

Step 1

Since $ f(x) = |x| $ when x is less than or equal to 0, we have $ f(x) = |0| = 0 $ when x approaches 0 from the left side. Show more…

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For ( f(x) = egin{cases} |x| & ext{if } x leq 0, \ sqrt{x} + 2 & ext{if } x > 0, end{cases} ) find: i. ( lim_{x o 0^-} f(x) ) ii. ( lim_{x o 0^+} f(x) ) For ( f(x) = x + 2 ) if ( x > 0 ), find: ( lim_{x o 0} f(x) )