Statement-1: The value of is equal to

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Statement-1: The value of lim⁡x→∞((x+2)tan⁡−1(x+2)−(xtan⁡−1x))\lim_{x \rightarrow \infty} ((x+2)\tan^{-1}(x+2) - (x\tan^{-1}x)) is equal to π\pi. Statement-2: If f(x)f(x) is derivable in [a,b][a, b] then ∃\exists atleast one c∈(a,b)c \in (a, b) such that f′(c)=f(b)−f(a)b−af'(c) = \frac{f(b) - f(a)}{b - a}. (a) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (b) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1 (c) Statement-1 is true, statement-2 is false. (d) Statement-1 is false, statement-2 is true.

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