Calculus Help

posted by .

Use f(x)= 1/(square root(x)+1) to answer the following;
-- Use the difference quotient f'(x)=lim z->x (f(x)-f(z))/ (x-z) to find f'(x)!

Please show steps!!!

Thank you!!!

  • Calculus Help -

    f(x) = 1/[ x^.5 +1 ]
    f(z) = 1/[ z^.5 + 1 }

    f(x)-f(z) = 1/[ x^.5 +1 ] - 1/[ z^.5 + 1]

    = ([z^.5+1]-[x^.5+1])/(x^.5z^.5 +x^.5+z^.5+1)

    = (z^.5-x^.5) /(x^.5z^.5 +x^.5+z^.5+1)
    Divide by (x-z) which is (x^.5-z^.5)(x^.5+z^.5)
    and get
    -(x^.5+z^.5) / (x^.5z^.5 +x^.5+z^.5+1)
    let z --->x
    - 2 x^.5 / (x +2 sqrt x + 1)
    check my arithmetic !!!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    What are the solution sets of the following 3 problems,the square root of x squared + 3x = x-3, the square root of 3x + 10 = x + 4 and finally the square root of 8x - 2 = the square root of 2x?
  2. Algebra

    Use the quadratic formula to solve the equation. Give exact answers: 2x^2 -1 = 6x. The choices are: a) -3 + square root(7)/2, -3 - square root(7)/2 b) 3 + square root(11)/2, 3 - square root(11)/2 c) 3 + square root(7)/2, 3 - square …
  3. Calculus

    How do I solve for lim h->0 (((a+h)^2 + 1)/(3(a+h)+7) - ((a^2 + 1)/3a + 7)) and then all divided by h?
  4. Math PLEASE HELP ASAP

    -PLEASE INCLUDE SOLUTIONS AND EXPLAIN HOW YOU DID IT PLEASE. *CHALLENGE. 1.SIMPLIFY : SQUARE ROOT OF 16^8+8^4/16^2+16^7 2.EXPRESS 1 + 1/1+SQUARE ROOT OF 2 - 1/1-SQUARE ROOT OF 2 IN THE FORM A+B SQUARE ROOT OF 2, WHERE A AND BARE RATIONAL …
  5. Math simplifying mixed radicals

    Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are supposed …
  6. Math Help!

    Four students worked to find an estimate for square root 22. Who is closest to finding the true estimate?
  7. Some Please Help me - PreCalc

    Verify that the point ( square root(31)/7, -3square root(2)/7 ) lies on the graph of the unit circle. If it does, use symmetry to find three other points that also lie on the graph of the unit circle. (direction - Type ordered pairs). …
  8. math

    Four students work to find an estimate for square root 54. Who is closest to finding the true estimate?
  9. Math

    Four students work to find an estimate for square root 27. Who is closest to finding the true estimate?
  10. Calculus AB

    Please help me with this WS 1) Find the value of lim as x-->-(square root of 3) of (-x^4 + 5x^2 -6)/(x+(square root of 3) 2) Find the distance between the discontinuities of g(x)= ((square root of x-4))/(x^2 -5x -1) 3)Find the value …

More Similar Questions