jason_r said:I have a function:
y=e^x
the tangent line at the point (1,e) would be x*e?
in order to find the area between the tangent line, the y-axis and y=e^x i equate these functions and solve for x?
I got this far
(e^x)/(x)=e
how do i solve for x
A tangent line is a line that touches a curve at a single point, without crossing over it. It represents the slope of the curve at that point.
To find the equation of a tangent line, you need to first find the slope of the curve at the point of tangency. This can be done by taking the derivative of the curve. Then, use the point-slope formula (y - y1 = m(x - x1)) with the coordinates of the point of tangency to find the equation of the tangent line.
Tangent lines and derivatives are closely related. The slope of a tangent line is equal to the value of the derivative at that point. In other words, the derivative gives us the slope of the curve at any given point, and the tangent line represents that slope at a specific point.
The area between two curves is the region bounded by the two curves on a graph. This area can be found by calculating the integral of the difference between the two curves over a given interval.
To find the area between two curves, you first need to determine the points of intersection between the two curves. Then, integrate the difference between the two curves with respect to the variable of integration, using the points of intersection as the limits of integration.