# 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 x       Solution

(8)  Evaluate the following limit

lim  x -> 0 tan 2x / sin 5x

(9)  Evaluate the following limit

lim  α -> 0 (sin αn)/ (sin α)m

(10)  Evaluate the following limit

lim  x -> 0 (sin (a + x) - sin (a - x))/ x

(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)

(13)  Evaluate the following limit

lim x-> 0  (1 – cos x)/x2

(14)  Evaluate the following limit

lim x-> 0  (tan 2x/x)

(15)  Evaluate the following limit

lim x-> 0  (2x – 3x)/x

(16)  Evaluate the following limit

lim x-> 0  (3x – 1)/√(x+1) – 1

(17)  Evaluate the following limit

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

(18)  Evaluate the following limit

lim x-> ∞  x (31/x + 1 – cos (1/x) – e1/x)

(19)  Evaluate the following limit

lim x-> ∞  {x [log (x + a) – log x] }

(20)  Evaluate the following limit

lim x-> π  sin 3x/sin 2x

(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  (ex - e-x) / sin x           Solution

(26)  Evaluate the following limit

lim x-> 0  (eax - ebx)/x         Solution

(27)  Evaluate the following limit

lim x-> 0  sin x (1 - cos x)/x3

(28)  Evaluate the following limit

lim x-> 0  (tan x - sin x)/x3

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