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

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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].
  • #1
Prototype44
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Homework Statement



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

Homework Equations


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
 
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  • #2
[itex]\lim_{h \to 0} \frac{\sqrt{x+h+1}-\sqrt{x+1}}{h}[/itex]

Have you tried multiplying the numerator and denominator by the conjugate of the numerator?
 
  • #3
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

Homework Equations





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.
 
  • #4
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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