No. This type of limit always is of the [0/0] indeterminate form.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
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.
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.
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.
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.
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.