Finding the Constant c for a Limit Problem

In summary, to find the constant c in the given limit problem, we must first factor the denominator and then find a value that makes the numerator equal to zero. This value is then set as c in order for the limit to exist.
  • #1
Kuma
134
0
limits problem solving help!

Alrighty so i have no idea where to even start...

Find the constant c such that

Lim
x-> 3

x^2+x+c
-----------
X^2 - 5x + 6


exists

Yeah so

so far i got as far as factoring the bottom

(x-3)(x-2)

And now i have no idea where to go from there
any ideas?
 
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  • #2


As x-->3, the denominator tends to zero, so for the limit to have the slightest chance to exist, the numerator must approach zero as well. For which value of c does it do so?
 
  • #3


require
(x-3)|(x^2+x+c)
that is find and "a" such that
(x-3)(x+a)=(x^2+x+c)
then set c=-3a
 

FAQ: Finding the Constant c for a Limit Problem

What is a limit in mathematics?

A limit in mathematics refers to the value that a function approaches as its input variable gets closer and closer to a certain value. It is a fundamental concept in calculus and is used to analyze the behavior of functions near a specific point.

Why is solving limits important?

Solving limits is important because it helps us understand the behavior of a function and its graph. It allows us to determine if a function has a limit at a certain point, and if so, what that limit is. This is crucial in many real-world applications, such as optimization problems and modeling physical phenomena.

What are the different techniques for solving limits?

There are several techniques for solving limits, including direct substitution, factoring, rationalization, and using algebraic manipulations. Other methods include using the squeeze theorem, L'Hôpital's rule, and the use of trigonometric identities. The appropriate technique to use depends on the type of limit and the given function.

How do you know if a limit does not exist?

A limit does not exist if the function does not approach a specific value as the input variable gets closer to a certain value. This can happen if the function has a vertical asymptote, an infinite or oscillating behavior, or if the left and right limits are not equal. In these cases, the limit is said to be undefined or does not exist.

Can limits be solved analytically?

Yes, limits can be solved analytically using algebraic manipulations and various techniques. However, there are some limits that cannot be solved analytically and require the use of numerical methods, such as graphing or using a calculator. These methods can provide a numerical approximation of the limit.

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