The positive number a does the curve intersect the line.
The expression of curve and line are y=ax and y=x respectively.
Consider y=ax and y=x
Hence, use the formulae of substitution
Now according to the given expression, the value of a is
At x=0 the value of a will touch the infinity hence x always greater than 0.
y=x is a straight line which passes through the origin point. Hence if x is not equal to zero then it will not intersect with the origin point.
Hence according to the a=eln|x|x
x is always greater than zero and
x∈(0,∞] where x is a real number.
The graph below clarifies the situation.
Conclusion: Hence the positive number a is eln|x|x