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Hey guys heres the problem,
lim (4x^2+9) / (3x^2 +5) = 4/3
x->infinity
find k, such that x> k/sqrt(epsilon) guarantees abs((4x^2+9) / (3x^2 +5) - 4/3) < epsilon
By removing the absolute sign and making the denominator common, we get
7 / (9x^2 + 15) < epsilon
keep solving we get
x > 1/3 sqrt(7/epsilon - 15)
Here is where I got stuck. How do we find k as a constant? 15 is inside the square root and if we want to make the whole thing as a fraction we would get x > 1/3 sqrt((7-15*epsilon)/epsilon). I can't just get rid of 15 either because that would screw up the inequality and I am meant to find the MINIMUM value of k. Any help would be appreciated.
Homework Statement
lim (4x^2+9) / (3x^2 +5) = 4/3
x->infinity
find k, such that x> k/sqrt(epsilon) guarantees abs((4x^2+9) / (3x^2 +5) - 4/3) < epsilon
Homework Equations
The Attempt at a Solution
By removing the absolute sign and making the denominator common, we get
7 / (9x^2 + 15) < epsilon
keep solving we get
x > 1/3 sqrt(7/epsilon - 15)
Here is where I got stuck. How do we find k as a constant? 15 is inside the square root and if we want to make the whole thing as a fraction we would get x > 1/3 sqrt((7-15*epsilon)/epsilon). I can't just get rid of 15 either because that would screw up the inequality and I am meant to find the MINIMUM value of k. Any help would be appreciated.