lim x infnitive (4x-1/2x+9)
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When you post a mathematical expression containing a fraction, you have to delimit the numerator and denominator using parentheses, otherwise the expression will be interpreted incorrectly most of the time.
For example, according to the usual rules of priority of operations, the posted expression evaluates to:
4x-(1/2)*x+9 = 7x/2+9
which is probably not quite what you want.
If the expression is meant to be:
(4x-1)/(2x+9), you can evaluate the limit by dividing both the numerator and denominator by x to get
(4-1/x)/(2+9/x)
and evaluate the expression when x->∞.
To find the limit of the function as x approaches infinity, you can analyze the behavior of the function as x becomes larger and larger.
In this case, you have the expression:
lim[x→∞] (4x - 1) / (2x + 9)
To evaluate this limit, divide both the numerator and denominator by x (the highest power of x).
lim[x→∞] (4x/x - 1/x) / (2x/x + 9/x)
This simplifies to:
lim[x→∞] (4 - 1/x) / (2 + 9/x)
Now, as x approaches infinity, 1/x approaches 0.
Therefore, the expression becomes:
lim[x→∞] (4 - 0) / (2 + 0)
Simplifying further:
lim[x→∞] 4 / 2
Finally, you get:
lim[x→∞] 2
So, the limit of (4x - 1) / (2x + 9) as x approaches infinity is equal to 2.