2 (2x -3x+5)(3x-1) 2 limx\to\infty 2 x is equal to : (3x +5x+4)\sqrt(3x+2)
Step-by-Step Solution
Key Concept: Apply the core result for standard limits and expansions and simplify using the given constraints.
(2x 2 - 3x + 5) (3x - 1) x/2 lim (3) x\to\infty (3x 2 + 5x + 4) \sqrt(3x + 2) x x x 2 3 5 1 2 x (2 - + ) (3x) 2 (1 - ) x x 2 3x = lim ⋅ x x x\to\infty 5 4 2 2 x (3 + + ) (3x) 2 2 x x 2 (1 + ) 3x x 1 x 1 2 limx\to\infty (1- -1)\times -1 3x 2 lim (1 - ) = e = e 6 x\to\infty 3x 2 limx\to\infty (1+ 2 -1)\times x 3x 2 lim (1 + ) = e x\to\infty 3x 1 = e3 -1 6 So, 2 3 \times e 1 = 2 3 \times 1 1 1 = 2 + 3\sqrte e3 e3 6
Correct Answer: 3