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Calculus/linear approximation

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Expert: Alon Mandes - 12/4/2009


Question
hello could you please point up the mistake i am doing in this question ?
Q)use linear approximation to estimate tan(44) ?
i started with :
f(x)= tan(x)      f(45)=1
f`(x)=sec^2(x)    f`(45)=2
L(x)=1+2(44-45)
tan(44)=-1
but of course that cant be true the answer must be something near 1 such as 0.9 !!
i appreciate you telling me what is wrong here !

Answer
f(x)=tang(x)
L(x)=f(xo)+f'(xo)(x-xo)
In our case , xo=45 , x=1 .
Therefore :
L(44)=tang(45)+sec^2(45)*(44-45)
L(44)=1+2(44-45). Now we have to transform -1 degrees into radians :
1/360=pi/a --> a=1130.97 --> 1 gegrees = 0.00277
Therefore : L(44)=1+2(-.00277)=0.9944 .

Alon.

Calculus

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Alon Mandes

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Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

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1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

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M.A in Mathematics & Bs.c in Electronics.

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