Desarrollo Guía De Actividades

DESARROLLO GUÍA DE ACTIVIDADES

FASE 1

A. Resuelva los siguientes límites:

1.

lim┬(x→2)⁡ (x^2-x-2)/(x^2-5x+6)=

lim┬(x→2)⁡ ((x-2)(x+1))/((x-3)(x-2))=

lim┬(x→2)⁡ ((x+1))/((x-3) )=(2+1)/(2-3)=-3

2.

lim┬(x→0)⁡ √(9+x-3)/x

lim┬(x→0)⁡ √(9+x-3)/x* (√(9+x)+3)/√(9+x+3)

lim┬(x→0)⁡ √(9+x)/ ((√(9+x)))/ (+3√(9+x)))/(3√(9+x+3)) (-3√(9+x-9))/

lim┬(x→0)⁡ (9+x-9)/(x√(9+x+3))=1/√(9+0+3)=1/√(5+3)=1/6

3.

lim┬(x→-2)⁡ (3-√(x^2+5))/(3x+6)

〖lim〗┬(x→-2)⁡((3-√(x^2+5))/(3x+6)) ((3-√((-2)^2+5))/(3(-2)+6))= (3-√(4+5))/(-6+6)= (3-√9)/(-6+6) = (3-3)/(-6+6)= 0/0 En el cual hay que factorizar

=〖lim〗┬(n→-2)⁡〖(3-√(x^2+5))/(3x+6) 〗. (3+√(x^2+5))/(3+√(x^2+5))

= 〖3^2-(√(x^2+5 ))〗^2/((3x+6)(3+√(x^2+5)))

= (9-x^2+5)/(3(x+2)(3+√(x^2+5)))

= (-x^2+14)/(3(x+2)(3+√(x^2+5)))

= (〖(-2)〗^2+14)/(3((-2)+2)(3+√(〖(-2)〗^2+5)))

= (〖(-2)〗^2+14)/(3((-2)+2)(3+√(〖(-2)〗^2+5)))

= 18/(3+√(4+5))

= 18/(3+3) 18/6 = 3

4.

lim┬(h→2b)⁡ (〖(b+h)〗^2-b^2)/h=

lim┬(h→2b)⁡ (〖(b+2h)〗^2-b^2)/2b=

lim┬(h→2b)⁡ (〖(3b)〗^2-b^2)/2b=(〖9b〗^2-b^2)/2b=〖8b〗^2/2b=4b

FASE 2.

5.

lim┬(x→0)⁡ tan7x/sen2x

Teniendo en cuenta que:

lim┬(q→0)⁡ senq/q=1

Entonces:

lim┬(x→0)⁡ tan7x/sen2x* (1/7x)/(1/2x) x 7/2=

lim┬(x→0)⁡ (tan7x/7x)/(sen2x/2x)* 7/2 = 1/1* 7/2= 7/2

6.

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