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Expert: Sherry Wallin - 9/30/2011


Question
please help me out with the following question please please.... I am waiting for the answer


Using the definition of the derivative as a limit, give a direct proof that

dw/dz = - 2/z3
when
w = 1/z2

Answer
Attir~
w = 1/z^2
lim   [f(z+h) - f(z)]/h = lim [1/(z+h)^2 - 1/z^2]/h => lim [z^2-(z+h)^2]/[h(z^2(z+h)^2)]
h->0  
all lim have h->0 under them          

lim [z^2 - (z^2+2zh+h^2)]/[hz^2(z+h)^2] => lim (z^2-z^2-2zh-h^2)/[hz^2(z+h)^2]
  => lim -h(2z+h)/[hz^2(z+h)^2] => lim -(2z+h)/[z(z+h)^2] => lim -(2z+0)/[z(z+0)^2]
  => -2z/zz^3 => -2/z^2

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

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I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

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Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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