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Calculus/2 Questions on Limits

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Expert: Alon Mandes - 1/20/2009


Question
Hi, I have these 2 questions on limits. I get half way through factoring before getting stuck...

1) lim (1/t) x {[1/(x+4)]-1/4}
  t->0

2) lim (1/t) x [root(t+9) - 3]
  t->0

Thanks

Answer
lim (1/t)[1/(t+4)-1/4]=
t->0
lim (1/t)[(4-t-4)]/[4(t+4)]=
t->0
lim (1/t)[-t/[4(t+4)]=
t->0
lim   -1/[4(t+4)] = -1/16.
t->0

-----------------

lim     (1/t)[√(t+9) - 3] =
t->0

lim     (1/t) * [√(t+9) - 3])*[√(t+9) + 3])/[√(t+9) + 3] =
t->0 =

lim    = (1/t) * [t+9 - 9])/[√(t+9) + 3] =
t->0

lim    = 1/[√(t+9) + 3] = 1/4
t->0

Alon.  

Calculus

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Alon Mandes

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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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