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24 October, 23:00

Is this right?

Which of the following is the best linear approximation for f (x) = tan (x) near x = 3pi/4?

I used the linearization equation y=f (a) + f' (a) (x-a)

y=f (3pi/4) + f' (3pi/4) (x-3pi/4)

y=tan (3pi/4) + sec^2 (3pi/4) (x-3pi/4)

y = - 1+2 (x-3pi/4)

y = - 1+2x-3pi/2

2y=4x-3pi-2

Is this correct?

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Answers (1)
  1. 24 October, 23:21
    0
    Yes you have the correct steps and answer. Nice job.

    Optionally, you can solve for y to get

    2y = 4x-3pi-2

    y = (4x-3pi-2) / 2

    y = 2x-1 - (3pi/2)

    which is another way to express the equation you got. There are many ways to write the answer.
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