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A comprehensive set of exercises focused on calculating limits, a fundamental concept in calculus. It includes a variety of problems ranging from basic to more complex, covering different techniques for evaluating limits, such as algebraic manipulation, trigonometric identities, and l'hôpital's rule. Each exercise is accompanied by a detailed solution, making it an excellent resource for students to practice and improve their understanding of limits. The exercises cover limits of trigonometric functions, limits involving indeterminate forms, and limits at infinity, offering a thorough review of essential calculus concepts. This resource is designed to help students develop problem-solving skills and gain confidence in their ability to tackle challenging limit problems.
Typology: Exercises
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x sin 7x
x^2 sin^2 x
3 sin^3 4 x
x sin 9x 2
x^2 sin^2 5 x
x 1 − cos 4x
x 1 − cos 5x
(^) xlim→ 0 x sin x + sin 7x
(^) xlim→ 0
sin 3x x
sin^2 5 x x^2
sin 8x sin 7x
sin 4x sin 8x
sin^3 4 x sin^3 2 x
1 − cos 4x 1 − cos 8x
sin 2x − x sin 3x − x
sin 3x + x sin 7x − sin 4x
(^2) x + sin (^2 3) x 4 x^2
sin^2 x − sin^2 2 x sin^2 x
n (sin 5x)m
p x^2 + sin x −
2 − sin x
p x^3 + x − 3
x − 1 sin(x − 2)
π/ 2 − x cos x
2 − cos x 2 x − π
cot 2x 1 − sin x
x^2 − 2 x sin 3x
(^) xlim→ 0 x^ sin^ x 1 − cos 2x + tan^2 x
(^) xlim→π^ π(π^ −^ x) sin x
(^) xlim→ 0
sin^2 x 1 − cos^2 (sin x)
x sin−^1 x
− (^1) x x
x sin 7x =
2 sin^2 x
x^3 sin^3 4 x
x sin 9x 2
x^2 sin^2 5 x
x 1 − cos 4x = 0
x 1 − cos 5x
x sin x + sin 7x
sin 3x x
x^2 sin^2 5 x
sin 8x sin 7x
sin 4x sin 8x
sin^3 4 x sin^3 2 x
1 − cos 4x 1 − cos 8x
sin 3x + x sin 7x − sin 4x =
x^2 tan^2 4 x
x^2 16 x^2
x 1 + tan x − 1 − tan x = undefined 0/^0
3 sin x − tan x cos x
x csc x − cot x
x^3 sin x − tan x
x sin 3x + sin x − 2 sin 2x
sec x − 1 2 x sin x
π · 1
x^2 − sin(x − 2) x^3 − x^2 − 2 =^
cot 2x 1 − sin x = 0
sin 5x x + 4
x^2 − 2 x sin 3x =
x sin x 1 − cos 2x + tan^2 x
(apply L’Hospital) =
π(π − x) sin x
1 − cos^2 (sin x) sin^2 x
= sin
(^2) (sin x) sin^2 x
arcsin x x = 1
arctan x x
