# Finding the Limit of f(x)=(x+1)^(1/2)

• Prototype44
In summary, this conversation discusses a limit problem involving the function f(x)=(x+1)^(1/2). The attempted solution involves simplifying the expression and using the conjugate of the numerator. However, the limit is still indeterminate at [0/0].
Prototype44

## Homework Statement

lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0

## The Attempt at a Solution

lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0

Should the answer be D.N.E because the square roots cancel each other and leave 0/0

Last edited:
$\lim_{h \to 0} \frac{\sqrt{x+h+1}-\sqrt{x+1}}{h}$

Have you tried multiplying the numerator and denominator by the conjugate of the numerator?

Prototype44 said:

## Homework Statement

lim f(x+h)-f(x)/h f(x)=(x+1)^(1/2) ans:1/2(x+1)^(1/2)
h→0

## The Attempt at a Solution

lim (x+h+1)^(1/2)-(x+1)^(1/2)/h lim (x+1)^(1/2)-(x+1)^(1/2)/h
h→0 h→0

Should the answer be D.N.E because the square roots cancel each other and leave 0/0
No. This type of limit always is of the [0/0] indeterminate form.

Figured it out

## What is a limit in calculus?

In calculus, a limit is a mathematical concept that describes the behavior of a function as the input approaches a particular value. It represents the value that a function "approaches" or gets closer to as the input gets closer to a specific value.

## How do you find the limit of a function?

To find the limit of a function, you can use the formal definition of a limit or evaluate the function at values closer and closer to the desired input value. You can also use algebraic or graphical methods to determine the limit.

## What is the limit of a square root function?

The limit of a square root function depends on the value of the input. If the input is a positive number, the limit will be the positive square root of that number. If the input is a negative number, the limit will be undefined.

## What is the limit of f(x)=(x+1)^(1/2) as x approaches infinity?

The limit of f(x)=(x+1)^(1/2) as x approaches infinity is infinity. This means that as the input value gets larger and larger, the output of the function also gets larger and larger without bound.

## What is the limit of f(x)=(x+1)^(1/2) as x approaches 0?

The limit of f(x)=(x+1)^(1/2) as x approaches 0 is 1. This means that as the input value gets closer and closer to 0, the output of the function gets closer and closer to 1.

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