Suppose c is an unknown number (but not a variable). Consider the following function: ¹a²+3, c+ 9, c²x², h (x) = x < 2 x = 2 x>2 Find the value(s) of c that makes lim h(x) exist. Use algebra, not a graph to justify your reasoning, though you may use a graph to check your work. →2
Suppose c is an unknown number (but not a variable). Consider the following function: ¹a²+3, c+ 9, c²x², h (x) = x < 2 x = 2 x>2 Find the value(s) of c that makes lim h(x) exist. Use algebra, not a graph to justify your reasoning, though you may use a graph to check your work. →2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose \( c \) is an unknown number (but not a variable). Consider the following function:
\[
h(x) =
\begin{cases}
\frac{1}{4}c^2x^2 + 3, & x < 2 \\
c + 9, & x = 2 \\
c^2x^2, & x > 2
\end{cases}
\]
Find the value(s) of \( c \) that makes \(\lim_{x \to 2} h(x)\) exist. Use algebra, not a graph to justify your reasoning, though you may use a graph to check your work.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe345ae0b-fd83-4d2e-a467-23dbb110ff23%2F80e7b457-1888-4c16-8b0a-45bfd0363734%2F4rn41as_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose \( c \) is an unknown number (but not a variable). Consider the following function:
\[
h(x) =
\begin{cases}
\frac{1}{4}c^2x^2 + 3, & x < 2 \\
c + 9, & x = 2 \\
c^2x^2, & x > 2
\end{cases}
\]
Find the value(s) of \( c \) that makes \(\lim_{x \to 2} h(x)\) exist. Use algebra, not a graph to justify your reasoning, though you may use a graph to check your work.
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