Question
Find the value of the constant $(a, b,$ orc $)$ that makes the function continuous.$$f(x)=\left\{\begin{array}{ll}2 x+9 x^{-1} & \text {for } x \leq 3 \\-4 x+c & \text { for } x>3\end{array}\right.$$
Step 1
This is given by the function $2x + 9x^{-1}$, so we substitute $x = 3$ into this function: $$\lim_{{x \to 3^-}} (2x + 9x^{-1}) = 2(3) + 9(3^{-1}) = 6 + 3 = 9.$$ Show more…
Show all steps
Your feedback will help us improve your experience
Suzanne W. and 75 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the value of the constant $(a, b,$ or $c)$ that makes the function continuous. $$ f(x)=\left\{\begin{array}{ll} 2 x+9 x^{-1} & \text {for } x \leq 3 \\ -4 x+c & \text { for } x>3 \end{array}\right. $$
Limits
Limits and Continuity
Find the value of constants c and d that make the function below continuous at x = 3. f(x) = x^2 - 5x, x < 3 c, x = 3 d + x, x > 3
Determine whether f(x)= is continuous at a) x = 1 b) x = 3
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD