Evaluate the limit of function (7x^2+5x)/(8x^3+6x), x-->infinity.
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
To evaluate the limit first we will divide by the highest power of the function which is x^3.
==> lim (7x^2+5x)/(8x^3+6x) = lim x^3(7/x+5/x^2)/limx^3(8+6/x^2)
==> lim (7/x +5/x^2)/ lim (8+6/x^2) = 0+0/(8+0)=0/8=0
Related Questions
- Calculate the limit n^2/( 1 + 2 + 3 + ... + n ), x->infinity
- 1 Educator Answer
- Find limits: 1.) lim x-->2 (8-x^3)/(x^2-5x+6) 2.) lim x-->-1 (x^2-5x+6)/(x^2-3x+2) 3.) lim...
- 2 Educator Answers
- limit x----> infinity ((x-5)/(x-2))^(x-3) is ?
- 1 Educator Answer
- Evaluate the limit (x^4-16)/(x-2), x-->2.
- 3 Educator Answers
- Calculate limit (x^2+2x+1)/(2x^2-2x-1), x->+infinity
- 1 Educator Answer
To find the lt(7x^2+5x)/(8x^3+6x), x-->infinity.
Solution:
As x approaches infinity both numerator and denominator goes to infinity. Being an indetrminate of the infinity/infinity form this could be solved by L' Hospial's rule of diffrentiating numerator and denominator and then taking the limit or dividing numerator and denominator by x^3 term by term and then taking the limit.
lt(7x^2+5x)/(8x^3+6x), x-->infinity.
= Lt (7x^2/x^3+5x/x^3)/(8x^3/x^3+6x/x^3) as x-->inf
=Lt(7/x+5/x^2)/(8+5/x^2) = (7*0+0)/(8+0) = 0/8 = 0
To evaluate the limit of the rational function, when x tends to +inf.,we'll factorize both, numerator and denominator, by the highest power of x, which in this case is x^3.
We'll have:
lim (7x^2+5x)/(8x^3+6x) = lim (7x^2+5x)/lim (8x^3+6x)
lim (7x^2+5x)/lim (8x^3+6x) = lim x^3*(7/x + 5/x^2)/lim x^3*(8 + 6/x^2)
After reducing similar terms, we'll get:
lim (7/x + 5/x^2)/lim (8 + 6/x^2)= (0+0)/(8+0)= 0/8= 0.
Student Answers