How to Solve a Limit Problem Involving Square Roots and a Constant

In summary, the limit of sqrt(r)/(r-9)^4 as r approaches 9 is infinite. This can be proven by showing that the numerator approaches 3 and the denominator approaches 0 as r approaches 9. It is also sufficient to show that the limit is the same from the left and right.
  • #1
synergix
178
0

Homework Statement


Lim sqrt(r)/(r-9)4
r->9

The Attempt at a Solution



I haven't been able to get started on this one I first tried to factor the bottom but I don't know how to or if that is even the right way to solve this problem. I am thinking maybe I have to multiply the bottom out but that seems a bit tedious.

is it sufficient to simply test from the left and right in order to get my answer?
 
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  • #2
this limit will be infinite, just by inspection

the numerator will be 3, whilst the denominator tends to 0

if you want to show it is unbounded, pick any positive number N, then show you can chose d, such that for |r-9|<d, then F(r) > N

but in answer to your question it is sufficient to show the limit is the same from the left & right
 

FAQ: How to Solve a Limit Problem Involving Square Roots and a Constant

What is a beginners limit problem?

A beginners limit problem is a mathematical problem that involves finding the value that a function approaches as its input approaches a specific value. This is referred to as the limit of the function.

How do you solve a beginners limit problem?

To solve a beginners limit problem, you can use algebraic techniques, such as factoring or simplifying the expression, or you can use graphical methods, such as graphing the function to see the behavior near the specific value. Additionally, you can use numerical methods, such as plugging in values that are very close to the specific value to approximate the limit.

What is the purpose of solving a beginners limit problem?

The purpose of solving a beginners limit problem is to understand the behavior of a function near a specific value. This can help us make predictions about the function's behavior and make calculations that may not be possible without the concept of limits.

What are some common mistakes when solving a beginners limit problem?

Some common mistakes when solving a beginners limit problem include not considering all possible algebraic and numerical methods, making arithmetic errors, and not understanding the concept of limits and how it applies to the problem.

How can beginners improve their skills in solving limit problems?

Beginners can improve their skills in solving limit problems by practicing a variety of problems, understanding the concept of limits and its applications, and seeking help from a tutor or teacher when needed. Additionally, they can use online resources and textbooks to learn and practice different techniques for solving limit problems.

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