Ap calculus ab study guide12/30/2023 ![]() ![]() On your exam, you may come across a piecewise function. This works for functions like polynomial, logarithmic, and exponential. (For instance: f(x)=x^2 for ), then the function will be continuous on that interval. If a function is defined only for a certain interval. We know a function is continuous at a certain point if the function continues and crosses that point without any break or interruption.įor instance, the function above is continuous at x=1 but not x=2. ![]() But just looking at the graph at f(x) will not give you the answer because there is a discontinuity there. ⚡️ Watch- AP Calculus AB/BC: Continuity, Part IĪs you can see, the double-sided limit here does exist because the function approaches the same value from both sides at x. If the limit of a certain function is too hard to solve for, you can solve for the limit of similar, easier functions to help you.ĭefining Continuity at a Point of Interval ⚡ Read- AP Calculus AB/BC: Squeeze TheoremĪnother way to solve for a limit is using the Squeeze Theorem. Then plug in the x value the limit approaches as x and that is your answer.ĭetermining Limits Using the Squeeze Theorem If you get 0/0, that means that you need to simplify the function before plugging in the x-value. When you have a double-handed limit to solve for, first try and plug in the value it is approaching as x. Not only can you find them on a graph or table, but you can find them algebraically! There are multiple ways we can solve for limits. For a left-handed limit, go from x values from negative infinity to 3 and for the right hand, look at the y values that correspond to the y values coming from 3 to positive infinity.ĭetermining Limits Using Algebraic Manipulation and Selecting Procedures for Determining Limits This can also be used to find single-handed limits. Since as x approaches 3, the y value is approaching 0.25, it is clear that as x approaches 3, the limit of the function on the table is 0.25. The function to the left should not influence your answer at all. If it has a positive sign, you only follow the function from your right-hand side and see what y value it approaches as it approaches a certain x value from the right side. Limits that have a positive or negative sign at the top of the x value it is approaching are called single-handed limits. Limits can be solved algebraically - simplify the function as much as possible, and when you are done, plug in the x value and you will get your answer! If you get an actual number, then that's your answer! Limits can be solved for on a graph- follow the function to as close to the x value it approaches as possible and then look at what value you have reachedĪlso, limits can also be solved for by plugging in the x value: Plug the x value into the function and if you get 0/0 or indeterminate, then solve for it algebraically. This means that as x approaches a, on the graph of f(x), the value on the y-axis that the function approaches is L
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