The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6. Find the fraction.
Answers
Step-by-step explanation:
l punto P(1,1/2) se encuentra en la curva y=x/(1+x).
a--Si Q es el punto (x,x/(1+x)), use su calculadora o algún aparato de cálculo para hallar la pendiente de la recta secante PQ (correcta a seis lugares decimales) para los siguientes valores de x:
(i) 0.5 (ii) 0.9 (iii) 0.99 (iv) 0.999
(v) 1.5 (vi) 1.1 (vii) 1.01 (viii) 1.001
b--Usando los resultados del inciso (a), calcule el valor de la pendiente de la recta tangente a la curva en (1,1/2) .
c--Usando la pendiente del inciso (b), encuentre una ecuación de la recta tangente a la curva en P(1,1/2).
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The point P (1,1 / 2) lies on the curve y = x / (1 + x).
a - If Q is the point (x, x / (1 + x)), use your calculator or some other computing device to find the slope of the secant line PQ (correct to six decimal places) for the following values of x:
(i) 0.5 (ii) 0.9 (iii) 0.99 (iv) 0.999
(v) 1.5 (vi) 1.1 (vii) 1.01 (viii) 1.001
b - Using the results of part (a), calculate the value of the slope of the tangent line to the curve at (1,1 / 2).
c - Using the slope from part (b), find an equation of the line tangent to the curve at P (1,1 / 2).