We will have our first midterm exam on Thursday (Oct 13). To prepare for the exam:
- review the following WebWork exercises
- Limits – Introduction: #5, 7, 8 (also solve the latter limit analytically!)
- Limits – Analytic: #2, 3
- Limits – One-Sided: #1-3
- Limits – Continuity: #1-2
- Derivative – Limit Definition: #2-3
- Derivatives – Functions: #2-3
- Derivatives – Power Rule: #2-9
- Derivatives – Power Rule – Part 2: #1-4, 6-7
- review Quiz #1 (solutions have been uploaded to Files)
- review the following concepts:
- the difference quotient, which gives the slope of a secant line:
![](https://openlab.citytech.cuny.edu/mat1475-ganguli-fall2022/files/2022/09/Screen-Shot-2022-09-28-at-3.13.15-PM.png)
![](https://openlab.citytech.cuny.edu/mat1475-ganguli-fall2022/files/2022/10/Screen-Shot-2022-10-12-at-10.20.02-AM-1024x483.png)
- the definition of the derivative as the limit of difference quotients, which gives the slope of the tangent line to the graph y = f(x) at the point (a, f(a)):
![](https://openlab.citytech.cuny.edu/mat1475-ganguli-fall2022/files/2022/10/Screen-Shot-2022-10-11-at-10.55.39-PM-1024x257.png)
![](https://openlab.citytech.cuny.edu/mat1475-ganguli-fall2022/files/2022/10/Screen-Shot-2022-10-11-at-10.55.47-PM-1024x94.png)
- finding the equation of the tangent line to y = f(x) at a point (x_1, f(x_1)) by using the point-slope equation of the line, with y_1 = f(x_1):
![](https://openlab.citytech.cuny.edu/mat1475-ganguli-fall2022/files/2022/10/Screen-Shot-2022-10-12-at-10.27.15-AM-1024x166.png)
See Examples 3.1 – 3.3 in Sec 3.1 and Example 3.22 from Sec 3.3:
![](https://openlab.citytech.cuny.edu/mat1475-ganguli-fall2022/files/2022/10/Screen-Shot-2022-10-12-at-10.31.08-AM.png)
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