Use the Limit definition to compute f\'(a) and find the equation of the tangent line for f(x) = x + x^-1, a=4 Solution f\'(x)= lim h approaches 0 of [f(x+h)- f(x)]/h So here we have ((x+h) + 1/(x+h) -x- 1/x )/h Simplifying and putting over a common denominator we have [h - h/x(x+h)]/h= 1 - 1/x(x+h) As h approaches 0 we have 1- 1/x^2 So f(4)= 1-1/16= 15/16 At (4, 17/4) we have 17/4 = 15/16 *4 +B B= 17/4-15/4= 2/4= 1/2 So equation of tanfent line is Y= 15/16 x +1/2.

1. Use the Limit definition to compute f'(a) and find the equation of the tangent line for f(x) = x +
x^-1, a=4
Solution
f'(x)= lim h approaches 0 of [f(x+h)- f(x)]/h So here we have ((x+h) + 1/(x+h) -x-
1/x )/h Simplifying and putting over a common denominator we have [h - h/x(x+h)]/h= 1 -
1/x(x+h) As h approaches 0 we have 1- 1/x^2 So f(4)= 1-1/16= 15/16 At (4, 17/4) we have 17/4
= 15/16 *4 +B B= 17/4-15/4= 2/4= 1/2 So equation of tanfent line is Y= 15/16 x +1/2