Find the Value Ofkso Thatfis Continuous Atx 2
Get the answer to your homework problem.
Try Numerade free for 7 days
Answer the question. 5) Is f(x) continuous atx 02 atx-2? X3 -<x $0 E(x) 3x, 0 gx < 2 2 <*44 X =2
Related Question
Problem 5: Forcing a piecewise function to be continuous_ Fill in the blanks. Show work in space provided. (a) Find values for Aand B so that f (x) is continuous for all values of x. A = B = Ax - 1, x < -1 f(x) = Bx2_ 1<* < 4 5 + Avx, x24 (b) Fill in the blank so that f (x) is continuous for all values of x. x2 _ 4 x #-2 x +2 f(x) X=-2
Discussion
You must be signed in to discuss.
Video Transcript
the objective of part A. Is to find the value of A and B. Such that the given function F. S continuous for all values of X. First of all understand that? Yes will be continuous At X is equal to -1. If we have limit Extends to -1 -1 and four picks which is nothing. But the left hand limit is equal to the right hand limit limit extends to minus one plus. Therefore fix. So let's compute the left hand limit and right hand limit from the given function. So it will be equal to eight times -1 minus one. This is the value of left hand limit and the right hand limit will be equal to B times minus one the whole square. So if we simplify this expression we will get minus a minus one is equal to B. This implies that the value of A plus one is equal to minus B, let's consider this equation as equation number one. And again the function F will be continuous at X is equal to four. If the left hand limit extends to four minus f of X is equal to the right hand limit limit extends to four plus F of X. So let's equip the correspondent left hand right hand limits. So we will have B times four square is equal to five plus eight times route four. So if we simplify this expression we will get 16 B is equal to five plus two. So let's consider this as a question # two. Now if we solve equation number one and two for the values of A and B we will get the required values of A. And B. So let's do that. Equation number two minus two times. Equation number one will give us 16 B plus two. B is equal to five plus to a minus two A minus one. This implies that B is equal to four by 18 which is equal to two. So let's substitute the value of B in equation number one, so we will get A plus one is equal to minus two by nine. This implies that the value of A is equal to -11 by night to the valuable A is -11 x nine and the value of B is two divided by nine. That makes the given function continuous at all values of X. Now let's move on to this second part. In the second part the objective is to fill in the blanks such that the given function F is continuous. It can be understood that the function F will be continuous everywhere implies that the function F is continuous at X is equal to -2. also We say F is continuous at X is equal to -2. If we have limit Extends to -2, therefore affects is equal to therefore minus two. From the given function. We can observe that the value will therefore fix Can be substituted here. So we have limit extends to -2, X squared minus four X-plus two is equal to 4 -2. And let's compute this limit. So we will have limit Extends to -2 X plus two times x minus two. The word advice X plus two. We are using the formula, esquire minus B squared is equal to a plus B times A -7. In our case A is X and B S. So X squared minus two squared, which is four can be written like this, So it will be equal to f of -2. So These two express tools will get canceled. So we'll have a limit of extends to -2. X -2 is equal to -2 -2, which is equal to -4. So the value of F of -2 is equal to -4. So The number that has to become in the blank will be -4. So this is the final answer. That's all.
Source: https://www.numerade.com/ask/question/answer-the-question-5-is-fx-continuous-atx-02-atx-2-x3-x-0-ex-3x-0-gx-2-2-44-x-2-80685/
0 Response to "Find the Value Ofkso Thatfis Continuous Atx 2"
Post a Comment