Question

26. Let $$f(x) = \begin{cases} \frac{1}{x} & \text{for } x \geq 1 \\ 2x + c & \text{for } x < 1 \end{cases}$$ a. Graph $f(x)$ when $c = 0$, and determine whether $f(x)$ is continuous for this choice of $c$. b. How must you choose $c$ so that $f(x)$ is continuous for all $x \in (-\infty, \infty)$?

Name: 26 let fx begincases frac1x textfor x geq 1 2x c textfor x 1 endcases a graph fx when c 0 and determine whether fx is continuous for this choice of c b how must you choose c so that fx is co 29305
Uploaded: 2021-07-31T13:12:16-08:00
Duration: 2 min 3 s
Channel: Yujie Wang
Description: 26 let fx begincases frac1x textfor x geq 1 2x c textfor x 1 endcases a graph fx when c 0 and determine whether fx is continuous for this choice of c b how must you choose c so that fx is co 29305

          26. Let
$$f(x) = \begin{cases} \frac{1}{x} & \text{for } x \geq 1 \\ 2x + c & \text{for } x < 1 \end{cases}$$
a. Graph $f(x)$ when $c = 0$, and determine whether $f(x)$ is continuous for this choice of $c$.
b. How must you choose $c$ so that $f(x)$ is continuous for all $x \in (-\infty, \infty)$?

$26 let fx begincases frac1x textfor x geq 1 2x c textfor x 1 endcases a graph fx when c 0 and determine whether fx is continuous for this choice of c b how must you choose c so that fx is co 29305$

Added by Francis F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Yujie Wang

07/31/2021

Step 1

When $c = 0$, the function becomes $$f(x) = \begin{cases} \frac{1}{x} & \text{for } x \geq 1 \\ 2x & \text{for } x < 1 \end{cases}$$ The graph of $f(x)$ consists of the graph of $y = \frac{1}{x}$ for $x \geq 1$ and the graph of $y = 2x$ for $x < 1$. Show more…

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26. Let $$f(x) = \begin{cases} \frac{1}{x} & \text{for } x \geq 1 \\ 2x + c & \text{for } x < 1 \end{cases}$$ a. Graph $f(x)$ when $c = 0$, and determine whether $f(x)$ is continuous for this choice of $c$. b. How must you choose $c$ so that $f(x)$ is continuous for all $x \in (-\infty, \infty)$?