Differentiating Logarithmic Functions without Base e - Page 10

Questions
  • #(dL)/L = \alphadT + 1/(sE_T)df \rightarrow ln(L/L_0) = \alpha\DeltaT + f/(sE_T)# Is that mathematically correct ?
  • #lim_(x->oo) x^(1/log_e x) = # ?
  • Lim without using de l'hospital method.. could you help?
  • Show that limit of log(2x-3)/2(x-2)=1 as x approaches to 2?
  • What is the logistic equation that satisfies the initial condition of (0,4) where the logistic differential equation is #dy/dt=y(1-y/36)#?
  • What is the value of #lim_(x->0)(2^x-1-x)/x^2# without using L'Hopital's rule and expansion of series?