CUET PG 2025 — Mathematics PYQ
CUET PG | Mathematics | 2025The value of limx→∞(1+3x2)x is:
Choose the correct answer:
- A.
e
- B.
e2
- C.
e32
(Correct Answer) - D.
e34
e32
Explanation
1. Di gayi limit:
x→∞lim(1+3x2)x
2. Standard Formula (1∞ form) ka istemal:
Agar limx→a[f(x)]g(x) ho, jahan f(x)→1 aur g(x)→∞, toh:
Limit=elimx→∞(f(x)−1)g(x)
3. Value rakhne par:
Yahan f(x)=1+3x2 aur g(x)=x hai.
Limit=elimx→∞(1+3x2−1)⋅x
4. Simplification:
Limit=elimx→∞(3x2)⋅x
x se x cancel karne par:
Limit=e32
Explanation
1. Di gayi limit:
x→∞lim(1+3x2)x
2. Standard Formula (1∞ form) ka istemal:
Agar limx→a[f(x)]g(x) ho, jahan f(x)→1 aur g(x)→∞, toh:
Limit=elimx→∞(f(x)−1)g(x)
3. Value rakhne par:
Yahan f(x)=1+3x2 aur g(x)=x hai.
Limit=elimx→∞(1+3x2−1)⋅x
4. Simplification:
Limit=elimx→∞(3x2)⋅x
x se x cancel karne par:
Limit=e32