Indeterminate Forms and de L'hospital's Rule - Page 4

Questions
  • How do you find #lim (sqrtx-1)/(x-1)# as #x->1^+# using l'Hospital's Rule or otherwise?
  • How do you use L'hospital's rule to find the limit #lim_(x->oo)x^(1/x)# ?
  • How do you use L'hospital's rule to find the limit #lim_(x->oo)x^3e^(-x^2)# ?
  • What is the limit as x approaches 0 of #sin(3x)/sin(4x)#?
  • How do you find #\lim _ { x \rightarrow + \infty } \frac { x } { \ln ( 1+ 3x ^ { 2} ) }#?
  • How do you find #lim sin^2x/x# as #x->0# using l'Hospital's Rule?
  • How do you find #lim t^2/(e^t-t-1)# as #t->0# using l'Hospital's Rule?
  • How do you find #lim (e^t-1)/t# as #t->0# using l'Hospital's Rule?
  • How do you find #lim_(theta->0) tantheta/theta# using l'Hospital's Rule?
  • Let a&b be real numbers such that lim_"x→0"(sin3x/x^3 + a/x^2 + b)=0?
  • Please help me to solve this problem? It's about real analysis. I am studying it for preparing my midterm.. Thank you very much for your help.
  • What is #lim x->1# of #sin(pix)/(x-1)#?
  • How do you calculate this limit without using l’Hospital’s rule: lim e^2x -1 / 3x as x → 0 ?
  • What are the values for h and k such that f(x) is both continuous and smooth at x=0?
  • Heello math friends! i have one question can we sue quotient rule in l hopital rule questions.?I have sent solution, plz have a look.If it is wrong plz solve it and any details answer in form of solve question and guidance would be great.
  • Is the function #(x^2-6x+9)/(x-3)# continuous?
  • What is the meaning of indeterminate form? And if possible a list of all the indeterminate forms?
  • What are the critical values, if any, of #f(x) = x^(7/3) - 7x^(1/3) #?
  • What is #lim_(x->4)# of #(x-4)/(sqrtx-2)#?
  • What is #lim x->2# of #(x^3-8)/(x-2)#?