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Consider the function f (x) = x/(2x+1)*2 . (i) Find the domain of this function. (Start...

Consider the function f (x) = x/(2x+1)*2 .

(i) Find the domain of this function. (Start by figuring out any forbidden values!)

(ii) Use (i) to write the equation of the vertical asymptote for this function.

(iii) Find the limits as x goes to positive and negative infinity,

(iv) Find the derivative of this function.

(v) Find the coordinates at point A(..,…), where the x-coordinate is 1. Use exact fractions, never a decimal estimate.

(vi) Find the equation of the tangent line at A. (NB: You first need its slope!) BE SURE TO SHOW ALL STEPS OF YOUR WORK WITH FRACTIONS.

(vii) Find the equation of the NORMAL line through A. (This is the line perpendicular to the tangent line. So what is its slope?) BE SURE TO USE FRACTIONS BUT NEVER MIXED NUMBERS. Show all of the fraction steps.

(viii) BONUS: See if you can put all the above info together and make a sketch of the function, showing everything you found out in the above problem.

Math   Precalculus   
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