Please explain and evaluate each of the following limits and show all the work

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anllre2130r

Mathematics

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so given f(x) = x - 4x^2

now f(x+h) = (x+h)  - 4(x+h)^2

                 =  (x+h) - 4(x^2 + h^2 + 2xh)

                = (x+h) -4x^2 - 4h^2 -8xh

so now limit h -->0  f(x+h) - f(x) / h   =  [  (x+h) - 4x^2 -4h^2 -8xh  - x +4x^2 ] / h

                                                           = [ h -4h^2 -8xh ] / h

                                                           = h [ 1 -4h -8x ] /h

                                                          = [ 1 -  4h -8x ]

so but h ->0 so plug h value

now we get =  1 - 4*0 -8x

                   = 1 - 8x


for the second one post it in another question I will answer thank you. comment for any doubts

Please let me know if you need any clarification. I'm always happy to answer your questions.


Anonymous
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