Getting Derivatives Using Limit Definition

Getting Derivatives Using Limit Definition

By Elo Cheng

​For this activity, we are going to practice a "see one, do one" concept where the first slide would contain a video of sample problem answered and explained then the following slide would be a similar problem to be answered by the student. You will set the pace on the progress of the slides. Make sure that you only proceed if you are ready to answer since you will only have 5 minutes for each of the problems. (There are only 4 problems for this activity.) Good luck!

Instructions

​https://www.youtube.com/watch?v=Hszu_Maneoo

Multiple Choice

$$\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$$  

• $$5x^2$$  

• $$10x$$  

• 10

• DNE

Multiple Choice

Using the limit definition of the derivative, find the derivative of $$f(x)=-4x$$  .

• 4
• x
• -4
• 0

Multiple Choice

Using the limit definition of the derivative, find the derivative of $$f(x)=x^3+x^2+3$$  

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Multiple Choice

Using the limit definition of the derivative, find the derivative of $$f\left(x\right)=\sqrt{x-7}$$  

• $$0$$  

• $$f'\left(x\right)=\frac{1}{2\sqrt{x-7}}$$  

• $$\frac{1}{\sqrt{x-7}}$$  

• $$\frac{1}{2}\sqrt{x-7}$$