The smallest distance between the point (0,0) and the curve y=e^x is 1 unit. This is because the curve intersects the y-axis at the point (0,1), making the shortest distance between the point and the curve 1 unit.
The smallest distance between (0,0) and y=e^x can be calculated using the Pythagorean theorem. We can draw a perpendicular line from the point (0,0) to the curve y=e^x, and this line will intersect the curve at the point (0,1). Then, we can use the formula d = √(x^2 + y^2) to calculate the distance, which in this case will be 1 unit.
Yes, the smallest distance between (0,0) and y=e^x will always be 1 unit. This is because the curve y=e^x is an exponential function that increases rapidly, so at any given point on the curve, the distance from (0,0) to that point will always be 1 unit.
No, the smallest distance between (0,0) and y=e^x cannot be negative. Distance is always a positive value, and in this case, the distance is 1 unit. Even if we consider the point (0,-1) on the curve, the distance from (0,0) to that point would still be 1 unit.
The value of e does not affect the smallest distance between (0,0) and y=e^x. The value of e only affects the steepness of the curve, but the distance between the point (0,0) and the curve will always be 1 unit, regardless of the value of e.