Podcast
Questions and Answers
Find lim_(x->0) (3 cosec 20 - 2 cot 30)
Find lim_(x->0) (3 cosec 20 - 2 cot 30)
3
Find lim_(x->0) (sin 7x - sin x) / sin 6x
Find lim_(x->0) (sin 7x - sin x) / sin 6x
7/6
Find lim_(x->0) (cosec x - cot x)
Find lim_(x->0) (cosec x - cot x)
0
Find lim_(x->0) (cos 7x - cos 9x) / (cos 3x - cos 5x)
Find lim_(x->0) (cos 7x - cos 9x) / (cos 3x - cos 5x)
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Find lim_(x->0) (3 sin x - sin 3x)/x^2
Find lim_(x->0) (3 sin x - sin 3x)/x^2
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Find lim_(x->0) (1 - cos^2 (kx)) / x^2, (k!=0)
Find lim_(x->0) (1 - cos^2 (kx)) / x^2, (k!=0)
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Find lim_(x->0) (1 - cos x) / x^2
Find lim_(x->0) (1 - cos x) / x^2
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Find (i) lim_(x->0) (1- cos 4x)/(1- cos 5x) (ii) lim_(x->0) (cos 2x - 1)/(cos x - 1)
Find (i) lim_(x->0) (1- cos 4x)/(1- cos 5x) (ii) lim_(x->0) (cos 2x - 1)/(cos x - 1)
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Find lim_(x->0) (1 - cos mx)/(1 - cos nx), where m and n are fixed non-zero real numbers.
Find lim_(x->0) (1 - cos mx)/(1 - cos nx), where m and n are fixed non-zero real numbers.
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Find lim_(x->0) (tan x - sin x)/x^3
Find lim_(x->0) (tan x - sin x)/x^3
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Find lim_(x->0) (sin (2+x) - sin (2-x))/x
Find lim_(x->0) (sin (2+x) - sin (2-x))/x
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Find lim_(θ->0) (1 - cos θ) / sin^2 2θ
Find lim_(θ->0) (1 - cos θ) / sin^2 2θ
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Find lim_(x->0) (tan^2 x - sin^2 x) / x^4
Find lim_(x->0) (tan^2 x - sin^2 x) / x^4
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Study Notes
Limits
- Finding limits: Various problems involve evaluating limits as x approaches a specific value (often 0).
- Trigonometric functions: Several problems utilize trigonometric functions like sine, cosine, tangent, cosecant, cotangent, and secant.
- Applications: These problems demonstrate the application of limit concepts and knowledge of known trigonometric identities to solve for specific values.
- 1-cos(kx)/x²: A common limit expression, demonstrating the use of special limit formulas and techniques.
- Non-zero real numbers: Some problems involve fixed non-zero real numbers (m and n) within the limits.
- 1-cos(mx): 1-cos(nx): Problems involving these expressions demonstrating trigonometric identities to solve for limits.
- cos(2x) - 1/cos(x) - 1: Another trigonometric expression, utilizing fundamental trigonometric concepts.
- (sin x)/x and (1-cos x)/x²: The concept of (sin x)/x approaching 1 as x approaches 0 is utilized in various problems, often in combination with other trigonometric functions.
- tan x - sin x/x²: This involves both logarithmic and trigonometric function limits applied together.
- 1-sec x/x²: A problem containing the secant function, showing how to evaluate limits involving secant.
- 1-cos(θ)/sin(2θ): A limit expression involving sine and cosine, demonstrating the technique for evaluating such expressions.
- tan²x - sin²x/x⁴: This example combines trigonometric functions and involves a higher-order term in the denominator, demanding careful manipulation to solve for the limit.
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Description
This quiz focuses on evaluating limits, particularly as x approaches specific values such as 0. It covers the application of trigonometric functions and identities in limit problems, including special limit expressions like (sin x)/x and (1-cos(kx))/x².
