Why in the world would you take any derivative?ugeous said:Remind me please, do you rewrite tan as sin/cos before taking derivative or after? I think it is before, but not 100% sure. Thanks
A limit is a mathematical concept that describes the behavior of a function as its input approaches a certain value. It is represented as the value that the function approaches, or the value it gets closer and closer to, as the input gets closer and closer to the given value.
To evaluate a limit, you must first plug in the given value into the function and see if it gives a meaningful result. If it does not, you may have an indeterminate form and will need to use other techniques such as factoring, rationalizing, or L'Hopital's rule to solve the limit. Otherwise, you can simply substitute the value and evaluate the function to find the limit.
There are several types of limits, including one-sided limits, infinite limits, and limits at infinity. One-sided limits only consider the behavior of the function from one side of the given value, while infinite limits describe the behavior of a function as it approaches infinity or negative infinity. Limits at infinity are limits where the input approaches infinity or negative infinity.
Some common techniques for evaluating limits include direct substitution, factoring, rationalizing, and using L'Hopital's rule. Other techniques include using trigonometric identities or using limits laws such as the sum, difference, product, and quotient laws.
To show reasoning when evaluating a limit, you can write out the steps you took to solve the limit, including any algebraic manipulations or other techniques used. You can also provide a graph or table to visually represent the behavior of the function as the input approaches the given value. Additionally, you can explain why certain techniques were used and how they help to solve the limit.