Find slope of tangent line on f



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Find slope of tangent line on f(x) =x2 at the point (1,1)



Find slope of tangent line on f(x) =x2 at the point (1,1)



Write the equation of tangent line

  • As the x value of the second point gets closer and closer to 1, the slope gets closer and closer to 2. We say the limit of the slopes of the secant is 2. This is the slope of the tangent line.

  • To write the equation of the tangent line use the point-slope formula









Limits

  • We write this as:



Graphical Analysis



Numerical Analysis



Numerical Analysis









Graph of f(x)



2.3 Functions That Agree at All But One Point



Analytic





Basic Limits







Analytic Techniques



Analytic Techniques

  • Rewrite algebraically if direct substitution produces an indeterminate form such as 0/0

  • Factor and reduce

  • Rationalize a numerator or denominator

  • Simplify a complex fraction



Find the indicated limit



Find the indicated limit



Find the indicated limit



































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