5. (10 points) Find the limit of √1+x y(x) = - X √I - X Use the binomial approximation for the square roots. For z << 1,

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5 10 Points Find The Limit Of 1 X Y X X I X Use The Binomial Approximation For The Square Roots For Z 1 1 (75.42 KiB) Viewed 21 times

5. (10 points) Find the limit of √1+x y(x) = - X √I - X Use the binomial approximation for the square roots. For z << 1, (1+z)² = 1 + nz (a) What is n for (1 + x) ? N=1/2 (b) What is z for (1 + x) ¾½ ? _z= › X (c) What is the binomial approximation of √/1 + x ? (1+x)¹½ = 1+1/2x (d) What is the binomial approximation of √//1 − x ?(1-x)¹/² = 1—-—-x 1 2 y(x) for x 0 two different ways. (e) What is y(x) using the binomial approximation? (f) Rationalize the numerator by multiplying the numerator and denominator by the factor √1 + x X [√1 + x + /1 − x ], i.e. + √I + √1 + x + x X - X * √1+x /1 + x X + √1 - X + - X