posted by .

find lim x->0 3- sqrt x+9/-x

  • calculus -

    In general, when there is a sum or difference of square-root terms, multiplying both numerator and denominator by the conjugate is a good strategy.

    Lim (3- sqrt( x+9))/(-x )
    = Lim (3-sqrt(x+9))(3+sqrt(x+9))/[(-x)(3+sqrt(x+9)]
    = Lim (9-(x+9))/[(-x)(3+sqrt(x+9)]
    = Lim (-x)/[(-x)(3+sqrt(x+9)]
    = Lim 1/(3+sqrt(x+9)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math calculus please help!

    l = lim as x approaches 0 of x/(the square root of (1+x) - the square root of (1-x) decide whether: l=-1 or l=0 or l=1 Let me make sure I understand the question. Do we have lim x->0 x/[sqrt(1+x) - sqrt(1-x)] ?
  2. calculus

    A sequence{an} is given by a1=sqrt(2), an+1=sqrt(2*an). a) by induction or otherwise, show that {an} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim n-->infinity an exists. b) Find lim …
  3. Calculus

    find lim f(x) - lim f(x) x->infinity x->-infinity if f(x)=ln (x+sqrt[x^2+a^2])/(x+sqrt[x^2+b^2]) a and b are real numbers
  4. Calculus

    show lim x->3 (sqrt(x)) = (sqrt(c)) hint: 0< |sqrt(x)-sqrt(c)|= (|x-c|)/(sqrt(x)+sqrt(c))<(1/(sqrt(c))*|x-c|
  5. Calculus

    show lim x->3 (sqrt(x)) = (sqrt(c)) hint: 0< |sqrt(x)-sqrt(c)|= (|x-c|)/(sqrt(x)+sqrt(c))<(1/(sqrt(c))*|x-c|
  6. Math(calculus)

    Evaluat d 4lowing1.lim x/|x| x-->0 2.lim x->1 sqrt(x^2+2- sqrt3)/x-1 3.lim n->~ f(n)=(1+1/n)^sqrtn 4. limx->0 f(x)= (12^x-3^x-4^x+1)/xtanx 5. Lim x->3 (x^n-3^n)^n/(n-3)^n
  7. Calculus

    Find the following limits algebraically or explain why they don’t exist. lim x->0 sin5x/2x lim x->0 1-cosx/x lim x->7 |x-7|/x-7 lim x->7 (/x+2)-3/x-7 lim h->0 (2+h)^3-8/h lim t->0 1/t - 1/t^2+t

    Could someone please solve these four problems with explanations?
  9. Check my CALCULUS work, please! :)

    Question 1. lim h->0(sqrt 49+h-7)/h = 14 1/14*** 0 7 -1/7 Question 2. lim x->infinity(12+x-3x^2)/(x^2-4)= -3*** -2 0 2 3 Question 3. lim x->infinity (5x^3+x^7)/(e^x)= infinity*** 0 -1 3 Question 4. Given that: x 6.8 6.9 6.99 …
  10. Math- Calculus

    I need help with these problems, I cannot find a similar example to help me in the book: 1. Find lim x->infinity (e^(-2x) + sin x). 2. Find the derivative of sqrt(9-x) using the limit process. 3. Find lim x-> -infinity (x + sqrt(x^2 …

More Similar Questions