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jaredjjj
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Have I solved this linear approximation question correctly?
To answer the second half do I have to use the formula f'(x)=sqrt(x^2+7) which would mean -2.8 would be approximately equal to 3.852 which is the same as 2.8.skeeter said:yes, $f(2.8) \approx -2.8$
now, how to determine if that value is an over or under estimate?
jaredjjj said:To answer the second half do I have to use the formula f'(x)=sqrt(x^2+7) which would mean -2.8 would be approximately equal to 3.852 which is the same as 2.8.
Linear approximation is a mathematical technique used to approximate the value of a function at a particular point by using the tangent line at that point. It is based on the concept of local linearity, where a small portion of a curve can be approximated by a straight line.
Linear approximation is different from other methods of approximation because it uses a linear function to approximate a non-linear function. This allows for a simpler and more accurate approximation compared to other methods.
The formula for linear approximation is y = f(a) + f'(a)(x-a), where f(a) is the value of the function at the point a, f'(a) is the derivative of the function at the point a, and x is the point at which the function is being approximated.
Linear approximation should be used when a function is too complex to be evaluated directly, but a good approximation is needed. It is also useful when finding the values of functions at points that are close to the known values, as the linear approximation is most accurate near the point of approximation.
You can check the accuracy of your answer using linear approximation by comparing it to the actual value of the function at the given point. If the difference between the two values is small, then the linear approximation is considered to be accurate.