(Solved):   In this question we will estimate the value \( \tan (0.327 x) \) using the linearization o ...

 

In this question we will estimate the value \( \tan (0.327 x) \) using the linearization of at the nearby point \( x=1 / 3 \). \[ f(x)=\tan (\pi x) \] a) Compute the derivative of \( f \) at \( 1 / 3 \). \[ f^{\prime}(1 / 3)= \] FORMATTING: \( \pi \) is written pi, \( \sqrt{a} \) is written sqrt(a). b) Write down the linearization \( L(x) \) of \( \tan (\pi x) \) at \( x=1 / 3 \) \( L(x)= \) FORMATTING: Give the exact value of all coefficients. c) Since \( 0.327 \) is near \( 1 / 3 \), we use the linear approximation of \( \tan (\pi x) \) found in (b) to estimate the value of tan \( (\pi x) \) at \( x=0.327 \). This gives \( \tan (0.327 \pi) \approx \) Number FORMATTING: Round your answer to at least six decimal places (You should check with your calculator and judge if this value is a good estimate.)