How to Multiply by a Conjugate with Multiple Terms?

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In summary, the conversation discusses how to multiply by a conjugate when there are more than two terms in the numerator of a limit problem. The suggested method is to simplify the problem by first solving for the limit h->0 3h/h=3, leaving the remaining problem as limit h->0 (sqrt(2x+2h)-sqrt(2x))/h.
  • #1
dimpledur
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multiplying by a conjugate??

Homework Statement



I am dealing with a limit, however, I am not sure how to multiply by a conjugate when there are two variables and three terms on top. For example

lim [3h + sqrt( 2x +2h) - sqrt( 2x)] / h
h->0


i don't need help solving it, i just need to know how would we multiply it by a conjugate when there are more than 2 terms?
 
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  • #2


I don't know how you got that but lim h->0 3h/h=3. There. Now you only have two terms in the numerator.
 
  • #3


how did you get h=3?, I tried the problem as well and got stuck.
 
  • #4


cam875 said:
how did you get h=3?, I tried the problem as well and got stuck.

I didn't get h=3. I got limit h->0 3h/h=3. That leaves you with figuring out limit h->0 (sqrt(2x+2h)-sqrt(2x))/h.
 

What is the purpose of multiplying by a conjugate?

Multiplying by a conjugate is a useful technique in mathematics, especially in algebra and trigonometry. It is used to simplify expressions, eliminate radicals, and solve equations.

What is a conjugate?

A conjugate is a pair of complex numbers that have the same real part but opposite imaginary parts. In other words, the conjugate of a+bi is a-bi, where a and b are real numbers.

How do you multiply by a conjugate?

To multiply by a conjugate, you simply multiply the first term of the expression by the conjugate of the second term, and vice versa. For example, to multiply (2+3i) by its conjugate (2-3i), you would multiply 2 by 2 and 3i by -3i, resulting in 4+9 = 13.

Why is multiplying by a conjugate helpful?

Multiplying by a conjugate helps to eliminate radicals in expressions, making them easier to simplify. It also helps to solve equations by getting rid of imaginary numbers and allowing us to work with real numbers.

Can you use multiplying by a conjugate in other areas of mathematics?

Yes, multiplying by a conjugate is a versatile technique that can be used in various areas of mathematics, such as complex numbers, trigonometry, and calculus. It is an essential tool for simplifying expressions and solving equations involving complex numbers.

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