Saturday

December 20, 2014

December 20, 2014

Posted by **cara** on Wednesday, September 2, 2009 at 2:51pm.

-> is an arrow(

lim x-> 0 (5x^3+8x^2)/ (3x^4 - 16x^2)

- math -
**MathMate**, Wednesday, September 2, 2009 at 3:22pmWhen both the numerator and denominator evaluate to zero or infinity, the limit can be found by applying the d'hÃ´pital rule.

The rule states that if the limit of a division is indeterminate, the limit of the derivatives of the numerator and the denominator will equal the limit in question. The rule can be applied successively until either the denominator becomes defined and non-zero.

For the case in point,

let

numerator=f1(x)=(5x^3+8x^2)

denominator=f2(x)=(3x^4 - 16x^2)

Since f2(0)=0, we need to find the derivative

f21(x)=d(f1(x))/dx=12x^3-32x.

Again f21(0)=0, so we find the derivative

f22(x)=d²(f2(x))/dx²=36x²-32

f22(0)=-32

Now we have to evaluate

f12(x)=d²(f1(x))/dx²=30x+16

f12(0)=16

Therefore the limit x→0

(5x^3+8x^2)/ (3x^4 - 16x^2)

=f12(0)/f22(0)

=16/(-32)

=-(1/2)

**Answer this Question**

**Related Questions**

calc - Use L’Hopital’s rule to find the limit of this sequence (n^100)/(e^n) ......

Calculus. Limits. Check my answers, please! :) - 4. lim (tanx)= x->pi/3 -(...

math - how do I solve this limit (-> is an arrow meaning "heading towards" ...

math - how do i find the limit of this? (This symbol:-> is an arrow) lim of x...

calc - need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting ...

math - the limit of cuberoot((-3x^3+5x+2)/(x^2-1)) as x approaches 3 is the ...

college math - Use a table to frind the indicated limit. 3 7. lim(4x ) x-2 2 8. ...

Calc Limits - lim (1+x)^1/x. Give an exact answer. x->0 This reads: The ...

MATH - Calculus (2) - if lim f(x) = a^3 x->a and if lim g(x) = a^2 x->a ...

Calculus - Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so ...