Find the Value of f(5) to Make f(x) Continuous at x=5

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The discussion focuses on determining the value of f(5) that ensures the function f(x) = (2x^2 + 3x - 65) / (x - 5) is continuous at x = 5. It is established that f(x) has a removable discontinuity at this point, and through factoring and direct substitution, the correct value for f(5) is determined to be 23. Participants also touch on related concepts such as horizontal asymptotes and polynomial limits, reinforcing the importance of continuity in function analysis.

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41. Find the Horizontal Asymptotes for17x/(x^4+1)^1/4 The answer I got is 17 and –17 . Can anyone correct me if I’m wrong?

62. f(x)= 4x^3+13x^2+11x+24 / x+3 when x<-3f(x)= 3x^2+3x+A when -3 less than or equal to xWhat is A in order for it to be continuous at -3?I don’t understand the top function but the bottom function I know is that I need to figure out the top and then make it equal to each other to find what A is since it only needs direct substitution

79. f is continuous at (-inf, + inf)f(y) = cy+3 range is (-inf,3)f(y) = cy^2-3 range is (3,+inf)what is C?C= 1 Am I correct?I did c(3)+3 and c(3^2)-3 and set them equal to each other and got 1.

81. Let f(x) = {2x^2+3 x -65) / (x-5)Show that f(x) has a removable discontinuity at x=5 and determine what value for f(5) would make f(x) continuous at x=5.Must define f(5)=The answer is 23? First I factored it and made it into 2x+13 and used direct substitution.Thanks for yoru time !
 
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Bump (10char) help please, this is dealing with asymptotes, polynomials and basically limits.
 

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