Question

The angle at which the curve y = e^x intersects the y-axis is
1) 0
2) π/4
3) π/2
4) π/6​

Answer 1

Answer:

1) 6

2) 3/4

3) 6/2

4) 2/6

Answer 2

Answer:

The angle at which the curve y = e^x intersects the y-axis is  π/2

The correct answer is Option (3)

Step-by-step explanation:

Hint:

The slope is absolutely relevant, but it's not the final answer; remember, you're looking for the angle. For example, a slope of 2 (not that this is the slope in your case) would correspond to an angle of 60∘, because that is the slope of a $30x^{0}-60x^{0} -90x^{0}$ right triangle in this position:

Slope of $f(x)=e^{x}$ at $(0,1)$ represents$\tan \theta$ where $\theta$ is the angle between curve and $x-$axis. To find you need to first find $\theta=\arctan \left(\frac{d y}{d x}(0,1)\right)$ and then required angle would be $\pi / 2-\theta$