whatlifeforme said:Homework Statement
evaluate.
Homework Equations
lim[itex]\displaystyle _{x->∞} \frac{2^x - 3^x}{3^x + 4^x}[/itex]
The Attempt at a Solution
i tried diving by highest term in denominator (4^x), but got me no where.
the solution manual has: (divided by highest term in numerator.)with the answer is zero which i don't know how.
lim[itex]_{x->∞}\displaystyle \frac{\frac{2^x}{3^x} - 1}{1 + \frac{4^x}{3^x}}[/itex] = 0
whatlifeforme said:Homework Statement
evaluate.
Homework Equations
lim[itex]\displaystyle _{x->∞} \frac{2^x - 3^x}{3^x + 4^x}[/itex]
The Attempt at a Solution
i tried diving by highest term in denominator (4^x), but got me no where.
the solution manual has: (divided by highest term in numerator.)with the answer is zero which i don't know how.
lim[itex]_{x->∞}\displaystyle \frac{\frac{2^x}{3^x} - 1}{1 + \frac{4^x}{3^x}}[/itex] = 0
The "Divided by highest term in numerator limit" refers to a mathematical concept in which the value of a function is calculated as the numerator approaches a certain value, typically infinity, and the denominator is divided by the highest power term in the numerator.
This limit is important because it helps us understand the behavior of a function as it approaches extreme values. It allows us to determine the overall trend of the function and make predictions about its behavior.
The "Divided by highest term in numerator limit" is different from other types of limits because it specifically focuses on the highest power term in the numerator, rather than the entire numerator or denominator. This allows us to simplify the calculation and make it easier to understand the overall behavior of the function.
The "Divided by highest term in numerator limit" is commonly used in physics and engineering to analyze the behavior of systems at extreme values. It is also used in economics and finance to make predictions about the growth or decline of a certain variable.
To solve a limit involving the "Divided by highest term in numerator limit", one can use algebraic manipulation to simplify the expression. This involves factoring out the highest power term and canceling out common factors. Then, the limit can be evaluated by plugging in the value that the numerator approaches.