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Shay10825
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Is there anyway to do this without calculatior and without graphing it?
lim (x-3)/(x-2)
x->2+
lim (x-3)/(x-2)
x->2+
JonF said:lim (x-3)/(x-2)
x->2+
in this case, the denominator approaches 0 while the numerator approaches 1. What happens to a fraction when it’s denominator gets small?
Shay10825 said:What if the limit of the numerator is 0 then what?
JasonRox said:What does "inf" mean?
JasonRox said:Can you tell me why that is?
Shay10825 said:But I don't understand how you would know the behavior of the graph without graphing it and using a calculator. How do you know the left and right don't equal without a graph or calculator?
To solve a limit without a calculator, you can use algebraic or graphical methods. Algebraic methods involve simplifying the expression algebraically, while graphical methods involve estimating the limit using a graph.
Solving a limit without a calculator helps develop a deeper understanding of the concept of a limit and allows for a more precise and accurate answer compared to using a calculator. It also helps to strengthen algebraic skills and problem-solving abilities.
Not all limits can be solved without a calculator. Some limits may require more advanced techniques such as L'Hopital's rule or Taylor series. However, most limits encountered in basic calculus courses can be solved without a calculator.
Some common mistakes when solving a limit without a calculator include forgetting to check the continuity of the function, not simplifying the expression fully, and not considering the behavior of the function near the limit point.
Yes, some tips for solving limits without a calculator include identifying and using known limits, factoring the expression, and using algebraic manipulation to simplify the expression. It is also important to carefully analyze the behavior of the function near the limit point.