A) \[0\]
B) \[2\]
C) \[1\]
D) \[1/2\]
Correct Answer: D
Solution :
| Let, \[y=\underset{x\to \infty }{\mathop{\lim }}\,\,\,\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+}}}}\] |
| \[\Rightarrow \,\,\,y=\underset{x\to \infty }{\mathop{\lim }}\,\,\,\sqrt{x+y}\] |
| \[\Rightarrow \,\,\,{{y}^{2}}=x+y\] |
| \[\Rightarrow \,\,\,{{\left( y-\frac{1}{2} \right)}^{2}}=\left( x+\frac{1}{4} \right)\] |
| \[\therefore \] vertex of parabola is \[\left( -\frac{1}{4},\frac{1}{2} \right)\] |
| Now, range of function i.e., \[y=\underset{x\to \infty }{\mathop{\lim }}\,\,\,f(x)=\frac{1}{2}\] |
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