Math 181 Honors Calculus

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tests solution

== test 1 ==

1)

    a)
    b)

2)a) f(x) = int(o,sqrtx)of e^t^2 dt

    chain rule 
    where u = squrt x
    using funamental therem of calc
    f(u)= int(0,u) of e^t^2 dt
    = e^u^2(1/2*x^(-1/2))
    = (e^x)/(2sqrt(x))

    b)lim of x as x goes to inf x/f(x)=
      lim of x as x goes to inf 1/f'(x)=
      lim of x as x goes to inf 1/(e^x/(2sqrt(x))=
      lim of x as x goes to inf (2sqrt(x))/(e^x)=
      lim of x as x goes to inf 1/(sqrt(x)e^x)=
      0

3)

4)

  v= 2pi*xbar*A
  v= int(a,b) of(2pi*x*(f(x)-g(x)))
  xbar= int(a,b) of(x*(f(x)-g(x)))/A

5)

 a)
 b)
 c)
 d)