2 different Calculus problems, help!?
March 22nd, 2010a) What are the vertical asymptotes.
b) What is the horizontal asymptote.
c) What are the x-intercepts?
d) What is the y-intercept?
2. Use linear approximation, i.e. the tangent line, to approximate 3sqrt27 as follows:
a) Let f(x)= 3sqrtx. The equation of the tangent line to f(x) at x=27 can be written in the form y=mx+b, find a and b
b) Using this, we find our approximation for 3sqrt27:
I've been trying over and over to find the right answer but I can't... Someone help me please? :(
(-8x-3)(8x-8)=0; Therefore, vertical asy. at -3/8 and 1.
1b). For horz asy, take the limit approaching -infinity and +infinity.
lim x>infinity [(x-8)(x+8)]/[(-8x-3)(8x-8)]. When taking the infinities, just look at the highest power, which just happens to be x^2 and -64x^2.
So, lim x>infinity [(x-8)(x+8)]/[(-8x-3)(8x-8)] = x^2/-64x^2 = -1/64
Doing this likewise for -infinity, you also get -1/64.
1c). x-ints are when f(x)= y = 0, so solving [(x-8)(x+8)]/[(-8x-3)(8x-8)] = 0 you get (x-8)(x+8)=0 (multiplying both sides by the function on the bottom).
Therefore, x-ints are at x = 8 and -8.
1d). Likewise, y-ints are when x = 0, which is just (-8)(8)/(-3*-8) = 64/24 = 8/3.
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