lim θ → 0 { [ θ n s i n θ ] + [ θ n t a n θ ] } = ____ where [x] is greatest integer ≤ x and n ∈ I

θ s i n θ → 1 as θ → 0 but 1

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsTrigonometric and Inverse Trigonometric limitsEasy2 minQB

MathematicsEasysingle choice

$lim_{θ \to 0} {[\frac{n s i n θ}{θ}] + [\frac{n t a n θ}{θ}]} =$ $____$ where [x] is greatest integer $\leq x$ and $n \in I$

Answer:

Solution:

$\frac{s i n θ}{θ} \to 1$ as $θ \to 0$ but < 1 $∴ [\frac{n sin θ}{θ}] = n - 1 [n \frac{Tan θ}{θ}] = n \frac{Tan θ}{θ} \to 1 as θ \to 0 but > 1$

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Trigonometric and Inverse Trigonometric limits

⏱ 2mℹ️ Source: QB

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