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 (2x – 3x)/x Solution
(16) Evaluate the following limit
lim x-> 0 (3x – 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 (31/x + 1 – cos (1/x) – e1/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 (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 Solution
(28) Evaluate the following limit
lim x-> 0 (tan x - sin x)/x3 Solution
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