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Calculus: Límites y Derivadas

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Calculus: Límites y Derivadas

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Quiz de cálculo diferencial e integral

Created by

Ana Ma Hdz
Ana Ma Hdz
Mexico

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Calculus: Límites y Derivadas
 

Calculus: Límites y DerivadasOnline version

Quiz de cálculo diferencial e integral

by Ana Ma Hdz
1

Evalúa el límite: lim_{x→1} (x^2-1)/(x-1).

2

Deriva f(x)=x^3 sin x.

3

Evalúa: ∫_0^1 2x dx.

4

Límite: lim_{x→2} (x^2-4)/(x-2).

5

Función f(x)=ln x. ¿Qué límite tiene x→0+?

6

Deriva e^{3x}.

7

Evalúa ∫_1^e dx/x.

8

Fundamental: ∫_a^b f(x)dx = ? si F' = f.

9

Si f(x)=x^2, ¿la derivada en x=2 es?

10

Límite: lim_{h->0} (sin h)/h.

Explicación

Al factorizar: (x-1)(x+1)/(x-1) = x+1, y al acercarse a 1, x+1 → 2.

Producto de x^3 y sin x: (x^3)' sin x + x^3 (sin x)'.

Integral de 2x es x^2; entre 0 y 1 da 1-0 = 1.

Factor: (x-2)(x+2)/(x-2) → x+2; en x→2 da 4.

Ln x se desploma a -∞ cuando x → 0+.}

La derivada de e^{ax} es a e^{ax}, con a=3.

Integral de 1/x es ln x; de 1 a e da ln e - ln 1 = 1-0 = 1.

La integral definida es F(b)−F(a) cuando F' = f.

La derivada de x^2 es 2x; en x=2 da 4.

Es la derivación básica de sin alrededor de 0: igual a 1.

 
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