
Understanding Differentiability and Continuity
Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard

Mia Campbell
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main goal of the video tutorial?
To discuss the applications of calculus
To explain the concept of limits
To prove that differentiability implies continuity
To prove that continuity implies differentiability
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is a way to find the derivative at a point?
Using the midpoint formula
Calculating the limit of the secant line's slope as it approaches the tangent line
Finding the slope of the secant line
Using the average rate of change
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean for a function to be differentiable at a point?
The function has a jump discontinuity at that point
The limit of the derivative exists at that point
The function is not defined at that point
The function is continuous everywhere
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is a characteristic of a point discontinuity?
The limit as x approaches the point is equal to the function's value at that point
The function has a vertical asymptote at that point
The function is continuous at that point
There is a gap in the function at that point
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the limit as x approaches C in a jump discontinuity?
The limit is infinite
The limit does not exist
The limit exists and equals the function's value at C
The limit is zero
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of continuity, what does it mean if the limit as x approaches C of f(x) equals f(C)?
The function is differentiable at C
The function has a jump discontinuity at C
The function is undefined at C
The function is continuous at C
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in proving that differentiability implies continuity?
Assume the function is continuous
Assume the function is differentiable
Calculate the derivative
Find the limit of the function
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