Question
For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the function is continuous, then what is the value of k?
NDA
Mathematics
Continuity and Differentiability
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 0.5
- B. 1
- C. 1.5
- D. 2
Answer
A. 0.5
Step-by-step solution
For the function to be continuous at x = 0, the left-hand limit must be equal to the right-hand limit and the value of the function at x = 0. Left-hand limit at x = 0 is given by: _ x 0^ - f(x) = _ x 0^ - 4(5^x) = 4(5^0) = 4 Right-hand limit at x = 0 is given by: _ x 0^ + f(x) = _ x 0^ + (8k + x) = 8k + 0 = 8k Equating the left-hand limit and the right-hand limit: 8k = 4 k = 4 8 = 0.5 Answer: 0.5
Related: Mathematics — Continuity and Differentiability · All PYQ Banks