Manipulating Limits Algebraically: Solving Tricky Equations

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Homework Help Overview

The discussion revolves around manipulating limit equations algebraically, specifically in the context of calculus. The original poster presents two limit problems that involve algebraic manipulation to evaluate them as the variable approaches specific values.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin solving the second limit problem and shares an attempt for the first limit involving a common denominator. Participants suggest using algebraic techniques such as multiplying by conjugates and expanding expressions.

Discussion Status

Participants are actively engaging with the problems, offering hints and suggestions for algebraic manipulation. There is a collaborative atmosphere as multiple participants propose similar strategies for approaching the problems, particularly regarding the use of conjugates.

Contextual Notes

The original poster mentions difficulty in formatting the equations in LaTeX, which may affect clarity in communication. There is also an indication of a learning context as the poster is brushing up on calculus before starting college.

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Homework Statement



Just brushing up on my calculus before I start college, but I'm having difficulty manipulating two different limit equations algebraically (sorry I can't find out how to put these into latex):

1) lim (t->0) {1/[t*sqrt(1+t)]} - (1/t)

2) lim (x->-4) [sqrt(x^2+9) - 5]/(x+4)

The Attempt at a Solution



don't know where to begin on (2), but for (1):

mult (1/t) by sqrt(1+t) to match denominators, left with [1 - sqrt(1+t)]/[t*sqrt(1+t)]

any hints?
 
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Try multiplying the numerator and denominator by 1+sqrt(1+t). Expand out the numerator and see what happens.
 
For 2), multiply the numerator and denominator by the conjugate of the numerator.
 
Dick said:
Try multiplying the numerator and denominator by 1+sqrt(1+t). Expand out the numerator and see what happens.

Bohrok said:
For 2), multiply the numerator and denominator by the conjugate of the numerator.

Ah, both of you were spot on with the conjugates. Thanks for your help.
 

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