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Questions and Answers
In calculus, the study of the rate of change is also known as Differential Calculus.
In calculus, the study of the rate of change is also known as Differential Calculus.
True (A)
The Identity Rule in calculus states that the derivative of a constant function is 0.
The Identity Rule in calculus states that the derivative of a constant function is 0.
False (B)
The Sum Rule in calculus states that the derivative of a sum of two functions is equal to the sum of their derivatives.
The Sum Rule in calculus states that the derivative of a sum of two functions is equal to the sum of their derivatives.
True (A)
According to the Constant Rule in calculus, the derivative of a constant multiple times a function is equal to the constant multiple times the derivative of the function.
According to the Constant Rule in calculus, the derivative of a constant multiple times a function is equal to the constant multiple times the derivative of the function.
According to the Difference Rule in calculus, the derivative of a difference of two functions is equal to the difference of their derivatives.
According to the Difference Rule in calculus, the derivative of a difference of two functions is equal to the difference of their derivatives.
The limit of a function as it approaches $c$ is always equal to its value at $c$.
The limit of a function as it approaches $c$ is always equal to its value at $c$.
The numerical representation of the limit of a function refers to the value that the function actually reaches.
The numerical representation of the limit of a function refers to the value that the function actually reaches.
The Limit Law states that the derivative of a constant multiple times a function is equal to the constant multiple times the derivative of the function.
The Limit Law states that the derivative of a constant multiple times a function is equal to the constant multiple times the derivative of the function.
A function must be defined at $f(c)$ for the limit of the function to exist as $x$ approaches $c$.
A function must be defined at $f(c)$ for the limit of the function to exist as $x$ approaches $c$.
As $x$ approaches 0, if $f(x)$ approaches 0.25 from both left and right sides, then the limit of $f(x)$ as $x$ approaches 0 is 0.25.
As $x$ approaches 0, if $f(x)$ approaches 0.25 from both left and right sides, then the limit of $f(x)$ as $x$ approaches 0 is 0.25.
Flashcards
Differential Calculus
Differential Calculus
The branch of calculus that focuses on the rate of change of functions.
Identity Rule
Identity Rule
The derivative of a constant function is always zero.
Sum Rule
Sum Rule
The derivative of the sum of two functions is the sum of their individual derivatives.
Constant Rule
Constant Rule
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Difference Rule
Difference Rule
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Limit of a function
Limit of a function
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Limit vs. Function Value
Limit vs. Function Value
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Two-Sided Limit
Two-Sided Limit
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Limit Existence
Limit Existence
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Limit from both sides
Limit from both sides
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Study Notes
Differential Calculus
- In calculus, the study of the rate of change is known as Differential Calculus.
The Identity Rule
- The derivative of a constant function is 0.
The Sum Rule
- The derivative of a sum of two functions is equal to the sum of their derivatives.
The Constant Rule
- The derivative of a constant multiple times a function is equal to the constant multiple times the derivative of the function.
The Difference Rule
- The derivative of a difference of two functions is equal to the difference of their derivatives.
Limits
- The limit of a function as it approaches c is always equal to its value at c.
- The numerical representation of the limit of a function refers to the value that the function actually reaches.
- For the limit of a function to exist as x approaches c, the function must be defined at f(c).
- If f(x) approaches 0.25 from both the left and right sides as x approaches 0, then the limit of f(x) as x approaches 0 is 0.25.
Limit Law
- The derivative of a constant multiple times a function is equal to the constant multiple times the derivative of the function.
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Description
This quiz covers the rules of limit laws, including the sum rule, difference rule, constant multiple rule, product rule, quotient rule, power rule, and root rule. Practice evaluating expressions with examples provided.
