뒤로Calculus I Test 1 Review: Limits, Continuity, Asymptotes, Derivatives
스터디 가이드 - 스마트 노트
자료에 맞춘 맞춤형 노트, 핵심 정의, 예시, 맥락을 확장해 제공합니다.
Q3. For the function whose graph is shown, find the following limits. If the limit does not exist, write DNE.
Background
Topic: Limits from a Graph
This question tests your ability to interpret a graph and determine the value of limits as approaches specific points from the left or right. It also checks your understanding of when a limit does not exist due to jumps, holes, or discontinuities.
Key Terms:
Left-hand limit (): The value approaches as comes from the left of .
Right-hand limit (): The value approaches as comes from the right of .
Limit at a point (): Exists if both left and right limits are equal.
DNE: "Does Not Exist" if the left and right limits are not equal or the function jumps/disconnects.
Step-by-Step Guidance
Examine the graph at each specified value. Identify whether the function approaches the same value from the left and right, or if there is a jump/discontinuity.
For each limit, determine if you are being asked for the left-hand limit (), right-hand limit (), or the two-sided limit ().
For left-hand limits, trace the graph as approaches the point from values less than . For right-hand limits, trace from values greater than .
If the graph has a hole, jump, or the left and right limits are not equal, the limit does not exist (DNE).
Write down the value the function approaches for each limit, or indicate DNE if appropriate. Stop here and try to match the graph to the limit values yourself.
Try solving on your own before revealing the answer!
Final Answers:
a) : 2
b) : 1
c) : 3
d) : 2
e) : 3
f) : DNE (left and right limits are not equal)
g) : DNE (left and right limits are not equal)
Each answer is based on the value the function approaches from the left and right at the specified values. If the left and right limits are not equal, the limit does not exist (DNE).
