pls solve for?

Question

lim x x ^4 - 3x ^3 + 2 / x ^3 - 5x ^2 + 3x + 1
x --->1

Answer 1

Lim (as x --> 1) of (x^4 - 3x^3 + 2) / (x^3 - 5x^2 + 3x + 1)

Notice that when x = 1, both the numerator and the denominator equal zero. Therefore, (x - 1) must be a factor of both terms.

Dividing out this factor in both terms gives :

(x^3 - 2x^2 - 2x - 2) / (x^2 - 4x -1)

Notice now, that when x = 1, both the numerator and the denominator do not equal zero. Therefore, there are no more factors in either term that equals (x - 1).

So now we can let x = 1 and substitute. This gives :

[1^3 - 2(1^2) - 2(1) - 2] / [1^2 - 4(1) - 1]
= -5 / -4
= 5 / 4, which is the limit as x --> 1.

Answer 2

limit=1-3+2/1-5+3+1=0/0
applying L Hospitals rule
limit=x>1 4x^3-9x^2/3x^2-10x+3
=1-9/3-10+3
=-8/-4=2 (answer)

Lim (as x --> 1) of (x^4 - 3x^3 + 2) / (x^3 - 5x^2 + 3x + 1)

Notice that when x = 1, both the numerator and the denominator equal zero. Therefore, (x - 1) must be a factor of both terms.

Dividing out this factor in both terms gives :

(x^3 - 2x^2 - 2x - 2) / (x^2 - 4x -1)

Notice now, that when x = 1, both the numerator and the denominator do not equal zero. Therefore, there are no more factors in either term that equals (x - 1).

So now we can let x = 1 and substitute. This gives :

[1^3 - 2(1^2) - 2(1) - 2] / [1^2 - 4(1) - 1]
= -5 / -4
= 5 / 4, which is the limit as x --> 1

Answer 3

lim x (x ^4 - 3x ^3 + 2)/(x ^3 - 5x ^2 + 3x + 1)
x --->1

This limit is of form 0/0 on substitution(x=1). Therefore you can directly apply L' Hospital's rule.

=>lim x (x ^4 - 3x ^3 + 2)/(x ^3 - 5x ^2 + 3x + 1)
x --->1

=>lim (5x ^4 - 12x ^3 + 2)/(3x ^2 - 10x + 3x)
x --->1

substituting x=1 =>(5-12+2)/(3-10+3)=-5/-4= 5/4

Answer 4

2

Answer 5

Simply substitute 1 for x. There are no parts to the equation you've presented where you have a zero in the denominator so
x^4=1
3x^3=3
2/x^3=2
5x^2=5
3x=3
so the equation is 1-3+2-5+3+1= -1

Answer 6

Yes, the above statements are right, use L'Hopital's Rule (I get 5/4), but I just wanted to add that it's always a good idea to include parenthesis when typing a function such as been written. (I assume, based on the context of the problem, I deduced that you meant (x ^4 - 3x ^3 + 2) /( x ^3 - 5x ^2 + 3x + 1), since otherwise the problem is trivial)

Just a friendly little tip to help make things a bit clearer.

Answer 7

limit=1-3+2/1-5+3+1=0/0
applying L Hospitals rule
limit=x>1 4x^3-9x^2/3x^2-10x+3
=1-9/3-10+3
=-8/-4=2 (answer)

Answer 8

Yes, use L'Hopital's Rule. However, i got 5/4.

And yes, parenthesis do help. I did this problem assuming that it was a fraction. If so, then it is 5/4

Answer 9

ahdjashda i cant make sure it out yet youve were given me questioning! haha im confident you dont care yet this jogs my memory of that riddle: its more effective than god extra evil than the devil the adverse have it the wealthy favor it and in case you eat it you die everybody's heard that... yet when your friends havent you may shoot it decrease back at em haha.. playstation ..? are you able to wager the answer...

Answer 10

divide the numerator by (x-1) and denominator by (x-1)
after that replace x by 1 and you will get your answer.