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Verify the given linear approximation at $ a = 0. $ Then determine the values of $ x $ for which the linear approximation is accurate to within 0.1.$ \ln (1 + x) \approx x $
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Calculus 1 / AB
Linear Approximation and Differentials
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In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
Verify the given linear ap…
we know the first thing we're gonna be doing is the natural log of one plus ear, which is just the natural above one which we know zero. Therefore, we know that the derivative is one over one plus acts. Now, remember, the natural log of one plus axe is equivalent to axe. So then, if we're able to graft this, it would look something like this. And we know that X would be between negative 0.3832 and 0.5162
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