For each of the following functions, use the limit definition of the derivative to compute the...

  

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For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) along with the appropriate tangent line to estimate the value of f'(a) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. a. f(x)= x-3x, a = 2 b. f(x) = 1, a = 1 c. f(x)=x, a = 1 d. f(x) = 2-x-1|, a = 1 e. f(x) = sin(x), a = / For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) along with the appropriate tangent line to estimate the value of f'(a) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. a. f(x)= x-3x, a = 2 b. f(x) = 1, a = 1 c. f(x)=x, a = 1 d. f(x) = 2-x-1|, a = 1 e. f(x) = sin(x), a = /