WBJEE · Maths · Application of Derivatives
Applying Lagrange's Mean Value Theorem for a suitable function \(f(x)\) in \([0, h],\) we have \(f(h)=f(0)+h f^{\prime}(\theta h), \quad 0 < \theta < 1 . \quad\) Then, for \(f(x)=\cos x,\) the value of \(\lim _{h \rightarrow 0^{*}} \theta\) is
- A 1
- B 0
- C \(1 / 2\)
- D \(1 / 3\)
Answer & Solution
Correct Answer
(C) \(1 / 2\)
Step-by-step Solution
Detailed explanation
We know that in a Lagrange mean value theorem there exist \(c \in(a, b)\) such that \[ f^{\prime}(c)=\frac{f(b)-f(a)}{b-a} \] \(\therefore \quad f^{\prime}(\theta h)=\frac{f(h)-\cos 0}{h-0}\)…
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