5 marks Q6. For what value(s) of $a$ and $b$ is the function $f(x)$ given below continuous at 0? $\begin{cases} arctan(\frac{1}{x}) & \text{if } x < 0\\a & \text{if } x = 0\\\frac{\sqrt{9 - bx} - 3}{x} & \text{if } x > 0 \end{cases}$

          5
marks
Q6. For what value(s) of $a$ and $b$ is the function $f(x)$ given below continuous at 0?
$\begin{cases}
arctan(\frac{1}{x}) & \text{if } x < 0\\a & \text{if } x = 0\\\frac{\sqrt{9 - bx} - 3}{x} & \text{if } x > 0
\end{cases}$

5
marks
Q6. For what value(s) of a and b is the function f(x) given below continuous at 0?
arctan((1)/(x)) if x < 0
a if x = 0
(√(9 - bx) - 3)/(x) if x > 0

Added by Guillermo M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

02/22/2023

Step 1

Step 1: For the function to be continuous at 0, the left-hand limit, right-hand limit, and the value of the function at 0 must be equal. Show more…

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5 marks Q6. For what value(s) of a and b is the function f(x) given below continuous at 0? $$f(x) = \begin{cases} \arctan\left(\frac{1}{x}\right) & \text{if } x < 0 \\ a & \text{if } x = 0 \\ \frac{\sqrt{9-bx-3}}{x} & \text{if } x > 0 \end{cases}$$