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3.10_3.11

# 3.10_3.11 - November 3rd 2008 Mathematics 140 Sections 3.10...

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November 3 rd 2008 Mathematics 140 Sections 3.10 & 3.11 (Linear approximations and Hyperbolic functions) Notes: Almost no one is here! I miss staring at the back of your head while you concentrate and look angelic Sections 3.10 - Linear Approximations and Differentials - Tangent lines to curves at specific points (usually defined by “a” - Increase in function from point “a” to “x” - (Tangent line approximations) - Ex. 28 pg. 252 - Use differentials (or, equiventlenty a linear approximation) to estimate the square root of 99.8 - Old techniques for when we did not need calculators - First of all, what is the function? - Left f(x) be root x - Point close to 99.8 is 100 and the root is 10 (Use this information) - Need the derivation of root x - f'(x) = 1/2sqrt(x) - f(x)-f(a)/(x-a) is approx f'(a) - we can use this ratio as an approximation - f(x) is approx. = f(a)+f'(a)*(x-a) = L(x) where L = linearisation of f - WHERE a = 11 and x = 99.8 - KNOW THIS STUFF DOM DOM! - 10+1/20(-0.2) = close to the root of 99.8 - The term DIFFERENTIAL - Precise definition which is premature of this class...

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