- #1
m_s_a
- 88
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Homework Statement
Find the limit :
http://www.a7bk-a-up.com/pic/uDs93333.bmp
http://www.a7bk-a-up.com/pic/zAP94166.bmp
The Attempt at a Solution
http://www.a7bk-a-up.com/pic/g0Q93947.bmp
Homework Statement
result
m_s_a said:Homework Statement
Find the limit :
http://www.a7bk-a-up.com/pic/uDs93333.bmp
http://www.a7bk-a-up.com/pic/zAP94166.bmp
The Attempt at a Solution
http://www.a7bk-a-up.com/pic/g0Q93947.bmp
Homework Statement
result
The Attempt at a Solution
m_s_a said:Last Qiustion:
http://www.a7bk-a-up.com/pic/Nww95795.bmp
Dick said:cos(pi/2)+i*sin(pi/2)=i, not i^(1/2). ?
Dick said:But what? Isn't the limit still 1?
m_s_a said:By imposing
I said let w=i===>w^2=-1
m_s_a said:Yes,
Find this limit
Dick said:Substitute zbar for z in the power series. What's wrong with that?
Dick said:Sure. |(sin(z*)/z*|=|sin(z)/z|. Because (sin(z)/z)*=(sin(z*)/z*) and |z|=|z*|. So you don't need analyticity, correct?
Dick said:Sure. Sorry, I'm not good at the script. afwan.
A complex function is a mathematical function that operates on complex numbers, which are numbers that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, equal to the square root of -1.
A limit of a complex function is the value that the function approaches as the input approaches a specific value. It is a fundamental concept in calculus and is used to analyze the behavior of functions at certain points.
The limit of a complex function can be found by evaluating the function at points close to the specified input value and observing the pattern of the output values. If the function approaches a specific value as the input gets closer and closer, that value is the limit. This can also be done algebraically using limit laws and techniques such as L'Hopital's rule.
Finding limits of complex functions is important because it allows us to understand the behavior of the function at specific points and to analyze its properties, such as continuity and differentiability. It also has practical applications in fields such as physics and engineering.
Some common strategies for finding limits of complex functions include using algebraic techniques such as factoring and rationalizing, using limit laws such as the sum, difference, and product rules, and using special techniques such as L'Hopital's rule. Graphing the function or using a table of values can also help in determining the limit of a complex function.