By utilizing the concept of a limit applied to the rate of change of a function, we are able to define the derivative in terms of a limit. This allows us to accurately calculate the slope of a function at any given point. Essentially, it is defined as the limit of (f(x+h)-f(x))/h as h tends towards 0.
| Topic | Problem | Solution |
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| None | a. Use the definition $m_{\tan }=\lim _{h \righta… | Given the function |
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1. Let |
Let's start by finding the values of |
| None | Find the derivative of the function using the def… | First, we find the derivative of the function using the definition of derivative. |
| None | Question 6 Find the (exact) direction cosines and… | Given the vector |
| None | 5 2 nd understand (R\&U): Stewart's pp 95-113 The… | The given limit is the definition of the derivative of a function at a point. |
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Consider the function |
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Let |
Let's consider the function |
| None | $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{\lef… | First, we need to simplify the expression inside the limit. We can do this by expanding the terms a… |
| None | Use the four-step process to find the slope of th… | Step 1: Calculate |
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Given the function |
The problem is asking for the difference quotient of the function |
| None | \( \frac{d f}{d t}=\lim _{h \rightarrow 0} \frac{… |