The statement is **True**.

### Explanation:
The derivative of a function at a certain point can indeed be defined using limits. This limit definition states that the derivative $ f'(a) $ of a function $ f $ at point $ a $ is given by the following formula:

$$
f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}
$$

This definition captures the notion of the instantaneous rate of change of the function at a specific point. It compares the change in the function's value $ f(a+h) $ as $ h $ approaches zero, thereby providing a precise mathematical way to determine the slope of the tangent line to the curve at the point $ a $.

In conclusion, this limit definition is fundamental in calculus and serves as the foundation for understanding derivatives, making the statement true.

Question

The statement is **True**.

### Explanation:
The derivative of a function at a certain point can indeed be defined using limits. This limit definition states that the derivative $ f'(a) $ of a function $ f $ at point $ a $ is given by the following formula:

$$
f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}
$$

This definition captures the notion of the instantaneous rate of change of the function at a specific point. It compares the change in the function's value $ f(a+h) $ as $ h $ approaches zero, thereby providing a precise mathematical way to determine the slope of the tangent line to the curve at the point $ a $.

In conclusion, this limit definition is fundamental in calculus and serves as the foundation for understanding derivatives, making the statement true.

Knowee AI · Accepted Answer

The statement is **True**.

### Explanation:
The derivative of a function at a certain point can indeed be defined using limits. This limit definition states that the derivative $ f'(a) $ of a function $ f $ at point $ a $ is given by the following formula:

$$
f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}
$$

This definition captures the notion of the instantaneous rate of change of the function at a specific point. It compares the change in the function's value $ f(a+h) $ as $ h $ approaches zero, thereby providing a precise mathematical way to determine the slope of the tangent line to the curve at the point $ a $.

In conclusion, this limit definition is fundamental in calculus and serves as the foundation for understanding derivatives, making the statement true.

The definition of the derivative of a function is also called the limit definition of the derivatives of a function. Group of answer choicesTrueFalse

Question

The definition of the derivative of a function is also called the limit definition of the derivatives of a function.

Solution

Explanation:

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