math
posted by gibbs .
Evaluate the following limits:
(I) Lim. (x+1)/[1sqrt(4+3x)]
X >1
(II) Lim. (23x5x^2)/(1+2x^2)
X >Infinite

rationalize the denominator
= (x+1)/[1√(4+3x)] * (1 + √(4+3x))/(1 + √(4+3x))
= lim (x+1)(1 + √(4+3x))/ (1  4  3x)
= lim (x+1)(1 + √(4+3x))/ (3(1+x)
= lim (1 + √(4+3x) )/3 , as x >1
= 2/3
Lim. (23x5x^2)/(1+2x^2) , X >Infinite
as x > infinity
the two terms that will "dominate" are 5x^2 on the top and 2x^2 at the bottom, the rest of the terms will become insignificant compared to their value
so we are left with 5x^2/(2x^2 or 5/2
so Lim. (23x5x^2)/(1+2x^2)
X >Infinite
= 5/2
Respond to this Question
Similar Questions

math
i need some serious help with limits in precalc. here are a few questions that i really do not understand. 1. Evaluate: lim (3x^32x^2+5) x> 1 2. Evaluate: lim [ln(4x+1) x>2 3. Evaluate: lim[cos(pi x/3)] x>2 4. Evaluate: … 
Calc. Limits
Are these correct? lim x>0 (x)/(sqrt(x^2+4)  2) I get 4/0= +/ infinity so lim x>0+ = + infinity? 
Maths Calculus Derivatives & Limits
Using the definition of the derivative evaluate the following limits 1) Lim h> 0 [ ( 8 + h )^1/3  2 ] / h 2) Lim x > pi/3 ( 2cosx  1 ) / ( 3x  pi) 
Calculus
Find the following limits algebraically or explain why they donâ€™t exist. lim x>0 sin5x/2x lim x>0 1cosx/x lim x>7 x7/x7 lim x>7 (/x+2)3/x7 lim h>0 (2+h)^38/h lim t>0 1/t  1/t^2+t 
Calculus
F(x)=x5 evaluate the following limits lim x>5 ( f(x)f(5))/(x5) lim x>5+ ( f(x)f(5))/(x5) 
math
Evaluate the following limits: (I) Lim. (x+1)/[1sqrt(4+3x)] X >1 (II) Lim. (23x5x^2)/(1+2x^2) X >Infinite 
math
Evaluate the following limits: (I) Lim. (x+1)/[1sqrt(4+3x)] X >1 (II) Lim. (23x5x^2)/(1+2x^2) X >Infinite 
math
Evaluate the following limits: (I) Lim. (x+1)/[1sqrt(4+3x)] X >1 (II) Lim. (23x5x^2)/(1+2x^2) X >Infinite 
Probability
Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success for each trial is 1/2 . Provide a numerical value, to a precision of 3 decimal places, for each of the following limits. 1. lim P … 
Math Limits
Let, f(x) = {4, x<5, 3x, x=5, 10+x, x>5} Evaluate each of the following: a) lim(x>5)f(x)= b) lim(x)5+)f(x)= c) f(5)=