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Calculus/l'hospital's rule
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Question
Hi Alon,
my question is:
how do I find the limit of this using hospital's rule?
I tried doing it by finding the derivative and I keep not getting a final number.
lim sin(10x)
x->0 ---------
tan(8x)
Also this problem, we never talked about using pi/2 in class.
lim 9cos(-5x)sec(9x)
x->(pi/2)
L'hospital's rule is applied whenever we have the form :
Lim [f(x)/g(x)] = 0/0
x->a
Now let's start out work :
Lim sin(10x)/tan(8x) =
x->0
According to L'hospital's rule :
Lim 10cos(10x)/[8/cos²(8x)] = 10/8
x->0
Lim 9cos(-5x)sec(9x) =
x->½π
Lim 9cos(-5x)/cos(9x) =
x->½π
According to L'hospital's rule :
Lim -45sin(-5x)/9sin(9x) =
x->½π
Lim -5sin(-5x)/9sin(9x) = -5/9
x->½π
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Answers by Expert:
Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
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1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
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M.A in Mathematics & Bs.c in Electronics.
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