anonymous
  • anonymous
use the definition of derivative to find f'(x) for f(x)=(3-5x)^1/2
Mathematics
schrodinger
  • schrodinger
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

bahrom7893
  • bahrom7893
limit definition is f'(x) = lim as h -> 0 [f(x+h) - f(x)]/h
bahrom7893
  • bahrom7893
plug that in: lim as h -> 0 {(3 - 5(x+h))^(1/2) - (3-5x)^(1/2)}/h
bahrom7893
  • bahrom7893
now to get rid of square roots, use the identity a^2 - b^2 = (a-b)(a+b) here you have a - b, but are missing a + b. So multiply top and bottom by: (3 - 5(x+h))^(1/2) + (3-5x)^(1/2)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

bahrom7893
  • bahrom7893
lim as h -> 0 [ (3 - 5(x+h))^(1/2) - (3-5x)^(1/2) * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ]/[ h * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ]
bahrom7893
  • bahrom7893
that is equal to the: lim as h -> 0 [ (3 - 5(x+h)) - (3-5x) ] / [ h * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ]
bahrom7893
  • bahrom7893
simplify numerator: lim as h -> 0 of [ (3 - 5(x+h)) - (3-5x) ] / [ h * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ] = = lim as h -> 0 of [ 3 - 5x-5h - 3+5x) ] / [ h * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ] = = lim as h -> 0 of [-5h]/[ h * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ]
bahrom7893
  • bahrom7893
Cancel out "h"s lim as h -> 0 of [-5h]/[ h * (3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ] = lim as h -> 0 of [-5]/[(3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ]
bahrom7893
  • bahrom7893
Plug in h = 0: lim as h -> 0 of [-5]/[(3 - 5(x+h))^(1/2) + (3-5x)^(1/2) ] = [-5]/[(3 - 5(x)^(1/2) + (3-5x)^(1/2) ]
bahrom7893
  • bahrom7893
As long as I didn't make any arithmetic/simplification errors, that is the answer, you can check it by taking the derivative directly. Please click on become a fan if I helped, I really want to get to the next level!! Thanks =)
anonymous
  • anonymous
thanx for ur reply

Looking for something else?

Not the answer you are looking for? Search for more explanations.