limit questions

1. lim(x->0) ln(1+2x) /x

= lim(x->0) 2/(1+2x)

= 2


2. lim(x->0) ((ln(x+a)-lna)) /x

= lim(x->0) 1/(x+a)

= 1/a

3. lim(x->0) (e^x^4-e^x^3)/5x^3

= lim(x->0) [(4x^3e^x^4)-(3x^2e^x^3)]/(15x^2)

= lim(x->0) [(12x^2+4x^3)e^x^4-(3x^2+6x)e^x^3]/(30x)

= lim(x->0) [(24x+12x^2)e^x^4+(12x^2+4x^3)(4x^3e^x^4)-(6x+6)e^x^3-(3x^2+6x)(3x^2)e^x^3]/30

= -6/30

= -1/5