The function f is defined by f(x)= (25-x^2)^(1/2) for -5 less than or = x less than or = 5
A) find f'(x)
B) write an equation for the tangent to the graph of f at x=3
C) let g be the function defined by g(x)= (f(x) for -5<or=x<or=-3)and (x+7 for -3<or=x<or=5)
D) find the value of the intagral 5 over 0 of x(25-x^2)^(1/2)dx

  1. 👍 0
  2. 👎 0
  3. 👁 311
  1. do you have no idea at all about any of these questions? Hard to believe this would come up till the topics have been covered. They look like pretty straightforward calculus and algebra operations.

    How far do you get?

    1. 👍 0
    2. 👎 0
  2. i found A and B, just checking if they're right. C i can never remember how to do these. D i haven't tried yet but i could probably figure out but i figured since i was putting the rest up i would do it as well

    1. 👍 0
    2. 👎 0
  3. There's nothing to figure out for C. They're just defining a new function. Not sure why it's even there.

    For D, it's pretty straightforward. Let
    u = 25-x^2
    then du = -2x dx and we have

    ∫[0,5] x√(25-x^2) dx
    = ∫[5,0] -1/2 √u du
    and it's clear sailing from there on

    1. 👍 0
    2. 👎 0
  4. thank youu

    1. 👍 0
    2. 👎 0
  5. A: d/dx √(25-x^2) = -x/√(25-x^2)

    B. At x=3, f(x)=4, so
    f'(3) = -3/4
    Now you have a point (3,4) and a slope: -3/4
    y-4 = -3/4 (x-3)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra

    The function h is defined by h(x)=x^(2)-x. Find h(2x).

    asked by Miranda on May 17, 2011
  2. Math - PreCalc (12th Grade)

    The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of the function at the right endpoint of the kth rectangle? A) 2+3k/n B) 4+3k/n C) 4+6k/n D) 5+6k/n

    asked by Shawna on March 21, 2014
  3. Calculus

    Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if

    asked by Hillary on September 24, 2009
  4. math

    what is the factorial of a negative number? The factorial function has singularities at the negative integers. You can see this as follows. For integers we define: (n+1)! = (n+1)n! and we put 0! = 1 So, from 0! you can compute 1!

    asked by chris on July 10, 2007
  1. Calculus - Functions?

    #1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of

    asked by Amy on February 21, 2011
  2. precalculus

    Suppose f is an even function and g is an odd function such that the composition fog is defined.d show that fog is an even function

    asked by Fatima on September 23, 2012
  3. calculus (gr 12)

    State the absolute maximum value and the absolute minimum value of each function, if the function is defined on the interval shown. {I CANNOT POST THE GRAPH SO CAN SOMEONE EMAll ME AT miss.a.parker at hot mail(. com) SO I CAN

    asked by HELP MEE PLEASE on April 17, 2013
  4. Calculus

    A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and

    asked by Leanna on February 9, 2011
  1. Calc

    g'(x)=tan(2/1+x^2) Let g be the function with first derivative given above and g(1)=5. If f is the function defined by f(x)=ln(g(x)), what is the value of f'(1)? I know the answer is 0.311, but I need steps as to why. Please and

    asked by Will on January 14, 2017
  2. algebra

    a function is defined by the equation y=8x-3. If the domain is 2≤x≤4, find the minimum value in the range of the function.

    asked by Carla on July 27, 2012
  3. math

    1)The function f is defined by the equation f(x)+ x-x^2. Which of the following represents a quadratic with no real zeros? A)f(x) +1/2 B)f(x)-1/2 C)f(x/2) D)f(x-1/2) 2) If I^(2k) = 1, and i = radical -1, which of the following

    asked by Aline on March 2, 2018
  4. Algebra/Math

    A function is defined as {(0,1)(2,3)(5,8)(7,2)}. Issac is tasked to create one more ordered pair for the function. Which ordered pair can he add the set to keep it a function. A. (7,0) B. (1,3) C. (0,2) D. (5,3) Please help! I'm

    asked by Quinn on November 1, 2018

You can view more similar questions or ask a new question.