LIMITS AND CONTINUITY WORKSHEET WITH ANSWER

(1) (a) Find the left and right limits of

f(x)  =  (x2 - 4) / (x2 + 4x + 4) (x + 3) at x  =  -2 

(b)  f (x) = tan x at x = π/2         Solution

(2)  Evaluate the following

 lim x->3 (x2 - 9) / x2(x2 - 6x + 9)         Solution

(3)  lim x-> [3/(x - 2) - (2x + 11)/(x2 + x - 6)]     Solution

(4)  lim x-> (x3 + x)/(x4 - 3x2 + 1)           Solution

(5)  lim x-> (x4 - 5x)/(x2 - 3x + 1)          Solution

(6)  lim x-> [(1 + x - 3x3)/(1 + x2 + 3x3)]           Solution

(7)  lim x-> [x3/(2x2 - 1) - x2/(2x + 1)]          Solution

(8)  (i)  Show that lim n-> (1 + 2 + 3 + .........+ n) / (3n2+ 7n +2)  =  1/6           Solution

(ii)  Show that lim n-> (12+22+.........+(3n)2) / (1+2+....+5n)(2n+3)  =  9/25          Solution

(iii)  Show that lim n-> (1/1⋅2 + 1/2⋅3 + 1/3⋅4+....+1/n(n+1))  = 1       Solution

(9)  An important problem in fishery science is to estimate the number of fish presently spawning in streams and use this information to predict the number of mature fish or “recruits” that will return to the rivers during the reproductive period. If S is the number of spawners and R the number of recruits, “Beverton-Holt spawner recruit function” is R(S) = S/(αS + where a and b are positive constants. Show that this function predicts approximately constant recruitment when the number of spawners is sufficiently large.     Solution

(10)  A tank contains 5000 litres of pure water. Brine (very salty water) that contains 30 grams of salt per litre of water is pumped into the tank at a rate of 25 litres per minute. The concentration of salt water after t minutes (in grams per litre) is C(t) = 30t/(200 + t).What happens to the concentration as  -∞       Solution

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. First Fundamental Theorem of Calculus - Part 1

    Apr 17, 24 11:27 PM

    First Fundamental Theorem of Calculus - Part 1

    Read More

  2. Polar Form of a Complex Number

    Apr 16, 24 09:28 AM

    polarform1.png
    Polar Form of a Complex Number

    Read More

  3. Conjugate of a Complex Number

    Apr 15, 24 11:17 PM

    conjugateofcomplexnumber1.png
    Conjugate of a Complex Number

    Read More