Question

Let \begin{equation} f(s) = \begin{cases} s^2 - c & \text{if } s \in ( -\infty, 4) \\ cs + 2 & \text{if } s \in [4, \infty) \end{cases} \end{equation} For what value of the constant $c$ is the function $f$ continuous on $(-\infty, \infty)$? $c = $ \\ Hint: Compute $\lim_{s \to 4^+} f(s)$ and $\lim_{s \to 4^-} f(s)$.

          Let \begin{equation*} f(s) = \begin{cases} s^2 - c & \text{if } s \in ( -\infty, 4) \\ cs + 2 & \text{if } s \in [4, \infty) \end{cases} \end{equation*} For what value of the constant $c$ is the function $f$ continuous on $(-\infty, \infty)$? $c = $ \\
Hint: Compute $\lim_{s \to 4^+} f(s)$ and $\lim_{s \to 4^-} f(s)$.

Let
f(s) = s^2 - c if s ∈ ( -∞, 4)
cs + 2 if s ∈ [4, ∞)
For what value of the constant c is the function f continuous on (-∞, ∞)? c =

Hint: Compute lims → 4^+ f(s) and lims → 4^- f(s).

Added by Jose Ramon C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Donna Densmore

02/22/2023

Step 1

This means that the left-hand limit and the right-hand limit must be equal at s = 4. Show more…

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Let $$f(s) = \begin{cases} s^2 - c & \text{if } s \in (-\infty, 4) \\ cs + 2 & \text{if } s \in [4, \infty) \end{cases}$$ For what value of the constant c is the function f continuous on (-∞,∞)? c = | Hint: Compute $$\lim_{s \to 4^+} f(s)$$ and $$\lim_{s \to 4^-} f(s)$$.