Evaluate lim (x→0) (sinh x – x) / ( sin x – x cos x)

Evaluate lim (x→0) (sinh x – x) / ( sin x – x cos x)

Question

Solution

Question

Evaluate lim (x→0) (sinh x – x) / ( sin x – x cos x)

Type 1 Problems

  1. Evaluate lim (x→0) (x e^x -log(1+x)) / x^2
  2. Evaluate lim (x→π/2) log(sin x) / (π – 2x)^2
  3. Evaluate lim (x→0) (sinh x – x) / ( sin x – x cos x)
  4. Evaluate lim (x→π/2) log(x-π/2) / tan x
  5. Evaluate lim (x→0) [a/x – cot x/a]
  6. Evaluate lim (x→0) [1/x – log(1+x)/x^2]

Type 2 Problems

  1. Evaluate lim x -> 0 (tan x – x)/(x ^ 2 * tan x)
  2. Evaluate lim (x->0) (x ^ 2 + 2 cos x – 2 ) / ( x sin^3 x)
  3. Evaluate lim (x->0) ((1/x^2)-(1/sin^2 x))
  4. Evaluate lim (x->0) ((1/x^2)-(cot^2 x))
  5. Evaluate lim (x->0) ((e^x – e^(-x) – 2 log(1+x)) / (x sinx) )
  6. Evaluate lim (x->0) ( (1 + sinx – cosx + log(1-x)) / (x tan^2 x) )

Type 3 Problems

  1. Evaluate lim(x→π/2)(sinx)^(tanx)
  2. Evaluate lim(x→0) (tanx/x)^(1/x)
  3. Evaluate lim(x→0) ((a^x+b^x)/2)^(1/x)
  4. Evaluate lim(x→0) ((a^x+b^x+c^x)/3)^(1/x)
  5. Evaluate lim(x→0) ((a^x+b^x+c^x+d^x)/4)^(1/x)
  6. Evaluate lim(x→0) [(sin^2(π/(2-x))]^sec^2(π/(2-x))

Related Topics

 

Leave a Reply