Resolver desigualdad. 0 "algo" distinto de cero. Es para acotar el resto de raíz de 2 en un pol. De Taylor de la función (1 + x) ^ (1 / 2) Centrado en 0, de orden 3. Entonces, si queda : [1 / t ^ (7 / 2)] > 0 no me sirve, porque me diría que el error es cero y eso no es cierto. Pregunta original : " Sea f(x) = (1 + x) ^ (1 / 2). Usando el pol. De Taylor de orden 3 de f en a = 0, calcular el valor aprox. De raiz de 2 que da dicho polinomio. Estimar el error. ".
En resumen
Derivemos <img src="https://tex.z-dn.net/?
Floresitalinda123
Derivemos
<img src="https://tex.z-dn.net/?f=f%28x%29%3D%281%2Bx%29%5E%7B1%2F2%7D%5C%5C%20%5C%5C%0Af%27%28x%29%3D%5Cdfrac%7B1%7D%7B2%7D%281%2Bx%29%5E%7B-1%2F2%7D%5Cto%20f%27%280%29%3D%5Cdfrac%7B1%7D%7B2%7D%5C%5C%20%5C%5C%0Af%27%27%28x%29%3D-%5Cdfrac%7B1%7D%7B4%7D%281%2Bx%29%5E%7B-3%2F2%7D%5Cto%20f%27%27%280%29%3D-%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%0Af%27%27%27%28x%29%3D%5Cdfrac%7B3%7D%7B8%7D%281%2Bx%29%5E%7B-5%2F2%7D%5Cto%20f%27%27%27%280%29%3D%5Cdfrac%7B3%7D%7B8%7D%5C%5C%5C%5C%5C%5C%0Af%5E%7Biv%7D%28x%29%3D-%5Cdfrac%7B15%7D%7B16%7D%281%2Bx%29%5E%7B-7%2F2%7D%5Cto%20f%5E%7Biv%7D%28t%29%3D-%5Cdfrac%7B15%7D%7B16%7D%281%2Bt%29%5E%7B-7%2F2%7D%5C%5C%5C%5C%5C%5C%0Af%28x%29%3D1%2B%5Cdfrac%7B1%7D%7B2%5Ccdot%201%21%20%7Dx-%5Cdfrac%7B1%7D%7B4%5Ccdot%202%21%7Dx%5E2%2B%5Cdfrac%7B3%7D%7B8%5Ccdot%203%21%7Dx%5E3%2BE_3%0A%0A" />
<img src="https://tex.z-dn.net/?f=f%28x%29%3D1%2B%5Cdfrac%7B1%7D%7B2%7Dx-%5Cdfrac%7B1%7D%7B8%7Dx%5E2%2B%5Cdfrac%7B3%7D%7B48%7Dx%5E3%2B%5Cleft%28-%5Cdfrac%7B15%7D%7B16%5Ccdot%204%21%7D%281%2Bt%29%5E%7B-7%2F2%7Dx%5E4%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%0Af%28x%29%3D1%2B%5Cdfrac%7B1%7D%7B2%7Dx-%5Cdfrac%7B1%7D%7B8%7Dx%5E2%2B%5Cdfrac%7B3%7D%7B48%7Dx%5E3%2B%5Cleft%28-%5Cdfrac%7B15%7D%7B256%7D%281%2Bt%29%5E%7B-7%2F2%7Dx%5E4%5Cright%29%5C%5C%20%5C%5C%0A%5Csqrt%7B2%7D%5Capprox%20f%281%29%3D1%2B%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B1%7D%7B8%7D%2B%5Cdfrac%7B3%7D%7B48%7D%5C%5C%20%5C%5C%0A%5Csqrt%7B2%7D%5Capprox%20%5Cdfrac%7B23%7D%7B16%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Csqrt%7B2%7D%5Capprox%201.4375%7D%0A" />
Cuyo error es
<img src="https://tex.z-dn.net/?f=E_3%3D-%5Cdfrac%7B15%7D%7B256%7D%281%2Bt%29%5E%7B-7%2F2%7D%5C%3B%2C%5C%3B%20t%5Cin%20%280%2C1%29%5C%5C%20%5C%5C%20%0A%5Cdfrac%7B1%7D%7B2%7D%5C%20%5Ctextless%20%5C%20%5Cdfrac%7B1%7D%7Bt%2B1%7D%5C%20%5Ctextless%20%5C%201%5Cto%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B2%7D%7D%5E7%5C%20%5Ctextless%20%5C%20%5Csqrt%7B%5Cdfrac%7B1%7D%7Bt%2B1%7D%7D%5E7%5C%20%5Ctextless%20%5C%201%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%7CE_3%7C%5Cleq%20%5Cdfrac%7B15%7D%7B256%7D%7D%0A" />
es decir
<img src="https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%3D1.4375%2BE_3" />.
Todo numero distinto de 0 elevado a la 0 es igual a : - - - > 1.
Si, da cero pues lo hice y me da ese resultado!
PORQUE EN UNA DIVICION, EL DENOMINADOR NUNCA PUEDE SER 0 LA DIVICION 0 NO ESTA DEFINIDAMENTE MAEMATICAMENETE.
Te refieres a dividir 1085 entre 15 y que de resto 0?