What is the limit definition of the derivative used for?

Understanding Derivatives Using the Limit Definition

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard

Mia Campbell
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
To find the integral of a function
To calculate the area under a curve
To determine the slope of a tangent line
To solve differential equations
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in using the limit definition to find the derivative of a function?
Substitute x with x + h in the function
Set the limit to infinity
Integrate the function
Find the second derivative
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When substituting x + h into the function, what should you be careful about?
Only substitute in the numerator
Substitute x + h for every x in the function
Substitute x + h only in the denominator
Do not substitute x + h at all
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of squaring the expression (x + h)?
x^2 + 2h + h^2
x^2 + h^2
x^2 + 2xh + h^2
x^2 + 2x + h^2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to distribute terms carefully when simplifying the expression?
To increase the degree of the polynomial
To ensure the function remains continuous
To make the function differentiable
To avoid errors in the final derivative
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the terms 3x^2 and -3x^2 when combining like terms?
They become 3x^2
They remain unchanged
They cancel each other out
They add up to 6x^2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of factoring out h from the numerator?
To simplify the expression and eliminate division by zero
To increase the degree of the polynomial
To make the function continuous
To find the integral of the function
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