How To Draw Tangent Line In Excel
Given a function, you tin can easily discover the slope of a tangent line using Microsoft Excel to practice the dirty piece of work. That is to say, y'all can input your 10-value, create a couple of formulas, and take Excel calculate the secant value of the tangent gradient. This is a fantastic tool for Stewart Calculus sections 2.1 and 2.2.
Notation that you lot can essentially enter the exact same functions into Google Sheets as well as Excel, and then this is a great tool for either option. So if yous have a Windows or Mac automobile with Excel installed, utilize that. If yous're running a Linux distro or Chrome Bone, or would rather use a free tool, use Google Sheets.
Getting Started
For this case, we'll use the post-obit function:
To translate, nosotros want the to find the slope of the tangent line of the function ii+SQRT(x) where x=1.
Step 1: Find the Y-Coordinate
Using the formula, information technology's quite unproblematic to find the y-coordinate based on the x-value. For example, for 10=ane, the y-coordinate would exist F(1)=ii+SQRT(1), leading to a value of 3.
Step 2: Secant Lines
At present nosotros'll need to use points both earlier and later on the x-value that approach that value, just never accomplish information technology (purple line beneath). Plotting these points on the graph will create the secant line for the formula.
At present it's time to offset plotting. We'll start with mitt calculations before moving on to using Excel (or Sheets) to automate the procedure.
Nosotros'll need to plot points for the x-value, the y-value, and the secant slope.
As you can come across to a higher place, with x=2, the y-value is 3.4142 (using the formula). The secant slope is calculated by taking the difference in the y-value and dividing it past the difference in the x-value, which is 0.4142.
Step three: Automate Y-Value with Excel
Call back that we desire the x-value to arroyo 1 without ever reaching it. And so, we can use two, 1.5, i.ane, 1.01, and 1.001. You lot'll also want to do this coming the other mode, so we can use 0, 0.5, 0.nine, 0.99, and 0.999.
Start by labeling the columns, then enter your x-values. We'll start with 2 as it approaches 1.
Now enter the formula to calculate the y-value. In the second cavalcade, input "=2 + sqrt(A2)" where A2 is the box where the x-value is stored (you can enter "A2" manually, or but click the box that contains the value), then hitting enter.
Now click on the box that you just entered the formula into, then drag from the bottom-correct of that box down to the final 10-value to insert the formula into each one—you'll notice the y-values pop up.
Pace four: Automate Secant Slope with Excel
At present in the tertiary column, let's enter the formula to calculate the secant slope. The formula here is "=(B2 - 3)/(A2 - ane)" (again, you tin simply click on the boxes that hold the value).
Simply every bit earlier, drag downward from the bottom-right to utilise the formula for the residuum of the x- and y-values.
Step five: Calculate for X-Values from 0 Approaching 1
Now just rinse-and-repeat, using x-values going the other way. Utilise the same elevate technique for these.
There y'all have it, the secant slopes for this formula when x=1. For a further detail, check out the video below.
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Source: https://ms-office.wonderhowto.com/how-to/create-tangent-line-with-excel-424513/
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