Textbook Question
Determine the following limits.
b. lim x→4^− x − 5 / (x − 4)^2
1. Limits and Continuity
Finding Limits Algebraically
2:53 minutesProblem 25a
Textbook Question
Determine the following limits.
a. lim z→3^+ (z − 1)(z − 2) / (z − 3)
Verified step by step guidance1
Step 1: Identify the type of limit problem. This is a one-sided limit as z approaches 3 from the right (z → 3^+).
Step 2: Analyze the behavior of the function as z approaches 3 from the right. The numerator (z - 1)(z - 2) is a polynomial that is continuous everywhere, so it will approach a finite value as z approaches 3.
Step 3: Consider the denominator (z - 3). As z approaches 3 from the right, (z - 3) approaches 0 from the positive side, which means the denominator is approaching zero.
Step 4: Determine the overall behavior of the function. Since the numerator approaches a finite value and the denominator approaches zero from the positive side, the limit will tend towards positive or negative infinity.
Step 5: Conclude the behavior of the limit. Since both (z - 1) and (z - 2) are positive when z is slightly greater than 3, the numerator is positive, and the denominator is positive, leading the limit to approach positive infinity.
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