) In class we showed that (1+ x)* ~ 1+ kx. (a) Using this formula estimate (1+ .01)10, (1 + .1)10, (1+ 1)1º, and (1+ 2)10. How do these estimates compare to the actual values from your calculator? (b) Give a range of values of x for which our formula (1+ x)* = 1+ kx work. (c) Show, using (1+x)* z 1+ kx, that 1+ (1+x)' + (1+ x)² + .. + (1+x)10 = 11 + 55x. Use this to estimate: 1+ 1.001 + 1.001² + 1.001³ + 1.0014 + .. +1.00110.
) In class we showed that (1+ x)* ~ 1+ kx. (a) Using this formula estimate (1+ .01)10, (1 + .1)10, (1+ 1)1º, and (1+ 2)10. How do these estimates compare to the actual values from your calculator? (b) Give a range of values of x for which our formula (1+ x)* = 1+ kx work. (c) Show, using (1+x)* z 1+ kx, that 1+ (1+x)' + (1+ x)² + .. + (1+x)10 = 11 + 55x. Use this to estimate: 1+ 1.001 + 1.001² + 1.001³ + 1.0014 + .. +1.00110.
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Transcribed Image Text:(6) In class we showed that (1+ x)* ~ 1 + kx.
(a) Using this formula estimate (1+.01)10, (1 + .1)1º, (1 + 1)10, and (1+ 2)10. How do
these estimates compare to the actual values from your calculator?
(b) Give a range of values of x for which our formula (1 +x)k = 1 + kx work.
(c) Show, using (1+x)* × 1 + kx, that
1+ (1+ x)' + (1+ x)² + ...
+ (1+x)10 = 11 + 55x.
Use this to estimate:
1+1.001 + 1.001² + 1.0013 + 1.0014 + ... + 1.00110.
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