# Tangent lines and areas between curves.

• jason_r
In summary, the conversation is discussing how to find the area between the tangent line of the function y=e^x at the point (1,e) and the y-axis. This can be done by equating the tangent line and the function and solving for x. However, the speaker is not sure how to solve for x and the other person suggests using integration.
jason_r
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

jason_r said:
I have a function:
y=e^x
the tangent line at the point (1,e) would be x*e?

Correct!

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

Thats not exactly it. Do you know how to integrate?

## 1. What is a tangent line?

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.

## 2. How do you find the equation of a tangent line?

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.

## 3. What is the relationship between tangent lines and derivatives?

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.

## 4. What is the area between two curves?

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.

## 5. How do you find the area between two curves?

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.

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