1. J


    1. lim(x->2) [(x+2)^1/2 - (3x-2)^1/2] / [(5x-1)^1/2 - (4x+1)^1/2] 2. lim(x->pi/2) [(2x - pi)^2 * (tan^2(x) + 1)]
  2. N

    One-Sided Limits with Sines and Cosines

    I am currently doing thee problems and know the answers (on answer key sheet given by teacher) and I don't know how to solve these. Can anyone possibly explain this to me? Thanks! Problem #1: lim (x->0) (1-cosx)/sinx Answer: 0 Problem #2: lim (x->0^+) (sin4x)/5x Answer: 4/5 Thanks!
  3. K

    Limits problems

    Using Taylor expansion of order 4, calculate the limit of quotient (tanx)^2 -3[(1+x^3)^1/3] +3 and 2ln(x^2 +cosx) -(sinx)^2.
  4. R

    Continuous limits

    Hallo! Please help as i am struggling with these for revision let f(x) = { 1, xEZ (x is subset of integers) 2, xE/Z (x is NOT subset of integers) } ^(looks like piecewise function) a) find lim x->3 f(x). hence find lim x-> a f(x) where a is subset of Z (integers) b) find lim x->pi f(x)...
  5. N

    Limits- do needful

    lim x -> 8_ [cube root of x] = _______. plz let me know method too. thanks in advance.
  6. R

    Manipulating limits

    Hallo! I need some help. lim x->4 ((2x^3-128)/(sqrt(x)-2)) i have tried manipulating the equation with conjugates but i just keep getting nowhere. wolfram has the limit at 384 please help!
  7. R

    Determining limits with use of L'Hopital's rule

    Hallo! Please help, i am struggling with these questions for revisions, and your solutions would be invaluable to me. Need to find the answers to these questions WITHOUT L'Hopital's rule A) lim x-> 0 (x^2 + |x|) cos (pi/x) B) lim x->0 ((e^(2x) - 1)/(e^(3x) - 1)) thank you in advance!
  8. H

    Hard limits of a piecewise function question

    Hi guys. Im stuck with this. consider this piecewise function: f(x) = {(a+bx), where x>2 3, where x = 2 b-ax, where x <2} determine the values for a and b which lim x -> 2 f(x) exists and is equal to f(2) thank you!
  9. H

    Defining limits question

    hi guys. Im struggling with a problem on limits. I've tried rearranging it a couple times but i keep hitting dead ends. Question is: lim (x->2) f(x) = ((x-2)|x-2|)/(x^2 -3x +2) Thanks for any help! :)
  10. A

    use formal definition for formal proof (limits)

    Use an appropriate formal definition to give a formal proof of each of the following. (a) lim (x^3? 5x+6) = 2 x?1 (b) lim 9-4x^2 = 6 x? ?1.5 3+2x (c) lim 1 = ? x? ?3 (x+3)^4 (d) lim lnx = - ...
  11. A

    some inequalities involving limits

    what's wrong here? I really appreciate your effort!
  12. M

    question on limits

    Hi, I am stuck with this question (see the attachment)....can anyone help me???
  13. M

    limits- please help

    can anyone help me with this??? lim (1 + q/x)^rx as x---> infinity
  14. M

    Double Integral from product of integrals, infinite limits From page 4 of this PDF. Can anyone help me understand what this significant challenge is?
  15. C


    What is the limit a_{n} = n^{1/n} how i can proof it ?
  16. M

    Limits 2

    lim x -> 81 (x - 81) / (?(x) - 9) I got 9 as the answer. I am not sure if that is correct or not.
  17. M


    How does lim x -> (-7) |x|/x equal 0? I assumed it equaled 1. Any help or advice would be much appreciated.
  18. K

    Help Appreciated ~ Graphing & Limits

    Plot the function f(x) over the interval [2.5,3.5]. Zoom in on the graph of the function to determine how close x must be to 3 in order that f(x) is within 0.015 of 15.
  19. M


    1. lim |x^2 + 49| / (x-7) - How do I factor this? x -> 7 I just want to double check these below, because I keep getting DNE (the limit does not exist): 2. lim (t^2 + t - 30)/(t - 6) = DNE t -> 6 3. lim (t^2 - 4t -11)/(t^2 - 16t +55) = DNE t -> 11...