LIMITS
Resources & Insights
Where the finite meets the infinite. Explore the elegant and precise world of limits—the core idea that makes calculus possible and unlocks continuous change.
Theorem# Limit of tanθ as θ → 0
Proof : We have, lim\(_{θ\to 0} { \dfrac {\mathrm tan \mathrm θ}{ \mathrm θ} } \) = lim\(_{θ\to 0} { \dfrac {\mathrm \sin \mathrm θ} {\mathrm θ \mathrm \cos\mathrm θ} } \) \( \{∵ \tan\theta = \dfrac {\sin\theta}{\cos\theta} \} \) = lim\(_ \mathrm {θ\to 0} \dfrac {\mathrm{\sin θ} } { \mathrm θ} \) × lim\(_ \mathrm {θ\to 0} \mathrm{cos θ} \) \( \{ ∵\) lim\(_{x\to y}f(x)g(x)\) = lim\(_{x\to y}f(x)\) . lim\(_{x\to y}g(x) \} \) = 1 × 1 = 1 Hence, lim\(_{θ\to 0} \tan\)θ = 1 READ MORE...
Theorem# Limit of cosθ as θ → 0
As θ → 0, we have cosθ → 1 Proof : When θ = 0, We have, lim\(_{θ\to 0} \cos \)θ = cos0 = 1 { ∵ cos0 = 1 } Hence, lim\(_{θ\to 0} \cos \)θ = 1 READ MORE...