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

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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.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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