#mat115

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Ley de L'Hôpital.

Ley de L’Hôpital.

La ley de L’Hôpital se aplica cuando, al evaluar un límite se llega a una forma indeterminada. La ley de L’Hôpital consiste en derivar el numerador y denominador como si fuesen funciones singulares. Formas indeterminadas. 0/0 ∞/∞ 0·∞ ∞-∞ 1^∞ ∞^0 0^0 Si se encuentra una forma indeterminada, se aplica la Ley de L’Hôpital siempre que esté en forma de cociente (las primeras dos). Llevar todas las…

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Transformaciones de funciones

Desplazamientos verticales de gráficas. Suponga que c>0. Para gráficas: y=f(x)+c, desplace c unidades hacia arriba la gráfica de y=f(x) y=f(x)-c, desplace c unidades hacia abajo la gráfica de y=f(x) Desplazamientos horizontales de gráficas. Suponga que c>0. Para graficar: y=f(x-c), desplace la gráfica y=f(x) a la derecha c unidades. y=f(x+c), desplace la gráfica y=f(x) a la izquierda c unidades.…

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Identidades trigonométricas

Algunas identidades trigonométricas. Identidades recíprocas. sinθ = 1/cscθ cosθ = 1/secθ tanθ = 1/cotθ cotθ = 1/tanθ secθ = 1/cosθ cscθ = 1/sinθ Identidades tangente y cotangente. tanθ = sinθ/cosθ cotθ = cosθ/tanθ Identidades pitagóricas. sin²θ + cos²θ = 1 1 + tan²θ = sec²θ 1 + cot²θ = csc²θ Fórmulas para negativos. sin(-t) = -sint cos(-t) = cost tan(-t) = -tant cot(-t) = -cott sec(-t) = sect…

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Relación entre un valor absoluto y una raíz cuadrada

Relación entre un valor absoluto y una raíz cuadrada

|x| = (x²)½ El valor absoluto de x es siempre positivo. La raíz cuadrada de x² no es siempre positiva. |x| = (x²)½ = { x si x≥0 -x si x<0 (x²)½ = { x si x≥0 -x si x<0 |x| siempre va a ser igual a (x²)½ Las dos van a depender de x si x≥0 o de -x si x<0 Posted from WordPress for Windows Phone

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Thanks for participating!

It has been an incredible academic year! Thank you all MAT096 and MAT115 participants!

We have learned a great deal from all that you shared and practiced on the blog.

Good luck with finals!

Best- Prof. Meangru and Prof. De León

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Practice Text

1.         Multiply and Simplify:           (a)  (4x -5)2                           

                                                              (b) (2x-5)(4x2 + 10x +25)

  2.         Divide                          (2x3 – 13x2 + 16x+ 9)   (x +5)

  3.         Find the equation of the line through (-4,0) and

            perpendicular to 2y = 4x – 6.

  4.         Given f(x) = x2  and g(x) = 3x + 10, compute the following

              (a)  f(-2)                                              (b) g(-2)

            (c)  f(-2) + g(-2)                                  (d) f(-2) g(-2)

  5.         Compute the composition f(g(5)) if f    f(x)= x2 -2x   

                and g(x) = 3x-5

  6.         Find the average rate of change of

            the function f over the indicated interval.

                                                            f(x) = 4x2 – 5x  ;  [1,2]

  7.         The price of a new item was $1000.

            After 5 years, the price dropped to $850. Assume the price decreased

            linearly. Let C represents the cost function after x years.

                          (a) Find a linear function (C = ax+b) for the price after x years.

            (b) Interpret the meaning of the values of a and b.

            (c) Use the linear function to find the cost after 7years.

  8.         Find the values of a and b in f(x) = ax + b, if f(-1) = 9 and f(2) = 3

  9.         In 2008 the cost of a new electronic game was $699.

            After 2 years, the cost increased to $899.

            Assume the cost increased linearly.

            Let C represents the cost function at any time x years.

                          (a) Find a linear function (C = ax+b) for the cost after x years.

            (b) Interpret the meaning of the values of a and b

            (c) Use the linear function to find the cost after 5years.