LIMITS AND CONTINUITY WORKSHEET WITH ANSWERS

To find the formulas please visit "Formulas in evaluating limits".

(1)  Evaluate the following limit 

lim  _{x -> ∞} (1 + 1/x)^7x               Solution

(2)  Evaluate the following limit 

lim  _{x -> 0} (1 + x)^1/3x           Solution

(3)  Evaluate the following limit 

lim  _{x -> ∞} (1 + k/x)^m/x         Solution

(4)  Evaluate the following limit 

lim  _{x -> ∞} [(2x² + 3)/(2x² + 5)]^(8x² + 3)          Solution

(5)  Evaluate the following limit 

lim  _{x -> ∞} (1 + (3/x)) ^{x + 2}       Solution

(6)  Evaluate the following limit 

lim  _{x -> 0} sin³ (x/2)/ x³          Solution

(7)  Evaluate the following limit 

lim  _{x -> 0} sin αx / sin ᵦx       Solution

(8)  Evaluate the following limit 

lim  _{x -> 0} tan 2x / sin 5x      Solution

(9)  Evaluate the following limit 

lim  _{α -> 0} (sin αⁿ)/ (sin α)^m      Solution

(10)  Evaluate the following limit 

lim  _{x -> 0} (sin (a + x) - sin (a - x))/ x      Solution

(11)  Evaluate the following limit 

lim  _{x -> 0} √(x² + a²) - a / √(x² + b²) - b    Solution

(12)  Evaluate the following limit 

lim _{x-> 0}  (2 arc sinx/3x)        Solution

(13)  Evaluate the following limit 

lim _{x-> 0}  (1 – cos x)/x²       Solution

(14)  Evaluate the following limit 

 lim _{x-> 0}  (tan 2x/x)        Solution

(15)  Evaluate the following limit

lim _{x-> 0}  (2^x – 3^x)/x       Solution

(16)  Evaluate the following limit

lim _{x-> 0}  (3^x – 1)/√(x+1) – 1       Solution

(17)  Evaluate the following limit 

lim _{x-> 0}  (1 – cos²x)/(x sin 2x)        Solution

(18)  Evaluate the following limit 

lim _{x-> ∞}  x (3^1/x + 1 – cos (1/x) – e^1/x)       Solution

(19)  Evaluate the following limit 

lim _{x-> ∞}  {x [log (x + a) – log x] }       Solution

(20)  Evaluate the following limit 

lim _x-> π  sin 3x/sin 2x       Solution

(21)  Evaluate the following limit 

lim _{x-> 0}  (1 + sin x)^{2 cosec x}         Solution

(22)  Evaluate the following limit 

 lim _{x-> 0} (√2 - √(1 + cos x)) / sin² x          Solution

(23)  Evaluate the following limit 

 lim _{x-> 0} (√(1+sinx) - √(1-sinx)) / tan x           Solution

(24)  Evaluate the following limit

lim _{x-> ∞}  {(x² – 2x + 1)/(x²-4x+2))^x           Solution

(25)  Evaluate the following limit

lim _{x-> 0}  (e^x - e^-x) / sin x           Solution

(26)  Evaluate the following limit 

lim _{x-> 0}  (e^ax - e^bx)/x         Solution

(27)  Evaluate the following limit 

lim _{x-> 0}  sin x (1 - cos x)/x³        Solution

(28)  Evaluate the following limit 

lim _{x-> 0}  (tan x - sin x)/x³        Solution

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