The notation we use is Graphs of Basic Functions Let c be a non-zero constant, r be any constant, and k be an integer. Roughly sketch the curve y = f(x), labeling asymptotes and intercepts. Then calculate the limits. 1. f(x) = 0 TY (1) lim f(x)= x-0 (2) lim f(x) = X-C M 2. f(x) = r Ty (1) lim f(x)= x-0 (2) lim f(x)= 34-X $ 3. f(x) = x TY (1) lim f(x) = x0 (2) lim f(x) = x-c
The notation we use is Graphs of Basic Functions Let c be a non-zero constant, r be any constant, and k be an integer. Roughly sketch the curve y = f(x), labeling asymptotes and intercepts. Then calculate the limits. 1. f(x) = 0 TY (1) lim f(x)= x-0 (2) lim f(x) = X-C M 2. f(x) = r Ty (1) lim f(x)= x-0 (2) lim f(x)= 34-X $ 3. f(x) = x TY (1) lim f(x) = x0 (2) lim f(x) = x-c
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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![### Understanding the Limit of a Function
**In your own words, describe the limit of a function \( y = f(x) \) as \( x \) approaches \( c \):**
*[Your explanation here]*
**The notation we use is:**
*[Notation]*
### Graphs of Basic Functions
Let \( c \) be a non-zero constant, \( r \) be any constant, and \( k \) be an integer. Roughly sketch the curve \( y = f(x) \), labeling asymptotes and intercepts. Then calculate the limits.
#### Graph Descriptions and Limits:
1. **\( f(x) = 0 \)**
- A horizontal line on the x-axis.
- (1) \( \lim_{x \to 0} f(x) = \underline{\quad\quad} \)
- (2) \( \lim_{x \to c} f(x) = \underline{\quad\quad} \)
2. **\( f(x) = r \)**
- A horizontal line at \( y = r \).
- (1) \( \lim_{x \to 0} f(x) = \underline{\quad\quad} \)
- (2) \( \lim_{x \to c} f(x) = \underline{\quad\quad} \)
3. **\( f(x) = x \)**
- A diagonal line through the origin with a slope of 1.
- (1) \( \lim_{x \to 0} f(x) = \underline{\quad\quad} \)
- (2) \( \lim_{x \to c} f(x) = \underline{\quad\quad} \)
Use these graphs to help understand the behavior of each function as \( x \) approaches different values.
*[Insert Specific Values for Blanks Based on Analysis Understanding]*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F739452bb-bec9-43d8-9372-35dc57efa9d5%2F73911161-79b0-4552-a484-b283b29ff432%2Fplh9s37_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Limit of a Function
**In your own words, describe the limit of a function \( y = f(x) \) as \( x \) approaches \( c \):**
*[Your explanation here]*
**The notation we use is:**
*[Notation]*
### Graphs of Basic Functions
Let \( c \) be a non-zero constant, \( r \) be any constant, and \( k \) be an integer. Roughly sketch the curve \( y = f(x) \), labeling asymptotes and intercepts. Then calculate the limits.
#### Graph Descriptions and Limits:
1. **\( f(x) = 0 \)**
- A horizontal line on the x-axis.
- (1) \( \lim_{x \to 0} f(x) = \underline{\quad\quad} \)
- (2) \( \lim_{x \to c} f(x) = \underline{\quad\quad} \)
2. **\( f(x) = r \)**
- A horizontal line at \( y = r \).
- (1) \( \lim_{x \to 0} f(x) = \underline{\quad\quad} \)
- (2) \( \lim_{x \to c} f(x) = \underline{\quad\quad} \)
3. **\( f(x) = x \)**
- A diagonal line through the origin with a slope of 1.
- (1) \( \lim_{x \to 0} f(x) = \underline{\quad\quad} \)
- (2) \( \lim_{x \to c} f(x) = \underline{\quad\quad} \)
Use these graphs to help understand the behavior of each function as \( x \) approaches different values.
*[Insert Specific Values for Blanks Based on Analysis Understanding]*
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