Limits
Easymathematics
The value of lim(x→2) (x² - 4)/(x - 2) is
Select the correct option:
Solution
Incorrect! Answer:
4
- Identify Indeterminate Form: Direct substitution of x=2 gives (22−4)/(2−2)=0/0, which is an indeterminate form.
- Simplification by Factorization: The numerator x2−4 is a difference of squares (x−2)(x+2).
- limx→2x−2(x−2)(x+2)
- Cancel Common Factors: For x=2, we can cancel (x−2).
- limx→2(x+2)
- Final Substitution: 2+2=4.
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More limits Practice Questions
MediumJEE-Advanced
Limit n→∞ of n1[(n+1)(n+2)...(n+n)]1/n is:
Limit n→∞ of n1[(n+1)(n+2)...(n+n)]1/n is:
View Solution→
HardJEE-Advanced
Let f(x) be a polynomial of degree 4 having extreme values at x=1 and x=2. If $\lim_{x \to 0} ...
Let f(x) be a polynomial of degree 4 having extreme values at x=1 and x=2. If $\lim_{x \to 0} ...
View Solution→
MediumJEE-Advanced
Evaluate the limit: L=limx→0secx−cosxln(1+x+x2)+ln(1−x+x2)
Evaluate the limit: L=limx→0secx−cosxln(1+x+x2)+ln(1−x+x2)
View Solution→
EasyJEE_MAIN
The value of lim(x→0) (sin x)/x is
The value of lim(x→0) (sin x)/x is
View Solution→
MediumJEE_MAIN
The value of lim(x→∞) (3x² + 2x + 1)/(2x² - x + 3) is
The value of lim(x→∞) (3x² + 2x + 1)/(2x² - x + 3) is
View Solution→
About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- limits
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
4
- Identify Indeterminate Form: Direct substitution of x=2 gives (22−4)/(2−2)=0/0, which is an indeterminate form.
- Simplification by Factorization: The numerator x2−4 is a difference of squares (x−2)(x+2).
- limx→2x−2(x−2)(x+2)
- Cancel Common Factors: For x=2, we can cancel (x−2).
- limx→2(x+2)
- Final Substitution: 2+2=4.
This easy difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of limits. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse limit, continuity and differentiability questions on RankGuru.