Question
Let k R . If _ x 0^+ ( ( k x)+ x+x)^ 2 x =e^6, then the value of k is
JEE Advanced
Mathematics
Limits
2024
JEE Advanced 2024 (Paper 2)
JEE Advanced Mathematics Question (2024) — Solution
Options
- A. 1
- B. 2
- C. 3
- D. 4
Answer
B. 2
Step-by-step solution
\( aligned & l= _ x 0^ + ( ( k x)+ x+x)^ 2 x =e^6 \\ & l= _ x 0^ + 2 x ( ( k x)+ x+x-1) \\ & l= _ x 0^ + 2 ( ( k x) k x k x k x k x x +1- (1- x) x^2 x ) \\ & l=2(k+1) \\ & l=e^ 2(k+1) =e^6 \\ & k+1=3 \\ & k=2 aligned \)
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