Let fx-x-12x-12x-12x-Compute the value of f100-f-100-

Let nbsp; y = f(x)=x+12x+12x+12x+.....∞=x+1x+y ⇒ y(x+y)=x(x+y)+1⇒ y^2 =x^2+1 Differentiating both side w.r.t x , we get 2ydydx=2x⇒ f(x).f' ...

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Algebra of Derivatives

Let fx=x+12...

Question

Let $f (x) = x + \frac{1}{2 x + \frac{1}{2 x + \frac{1}{2 x + . . . . . \infty}}}$
Compute the value of $f (100) . f^{'} (100) .$

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f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & x & x + 1 2 x & x (x - 1) & (x + 1) x 3 x (x - 1) & x (x - 1) (x - 2) & (x + 1) x (x - 1) \end{matrix} ∣ ∣ ∣ ∣ ∣

f (100)

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + s i n^{2} x & c o s^{2} x & 4 s i n 2 x s i n^{2} x & 1 + c o s^{2} x & 4 s i n 2 x s i n^{2} x & c o s^{2} x & 1 + 4 s i n 2 x \end{matrix} ∣ ∣ ∣ ∣ ∣

f (x) =

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - sin π x}{1 + cos 2 π x}, & x < \frac{1}{2} p, & x = \frac{1}{2} \frac{\sqrt{2 k + \sqrt{2 x - 1}} - 2}{\sqrt{2 x - 1}}, & x > \frac{1}{2} \end{matrix}

f

x = \frac{1}{2},

k + 12 p

f : [- \frac{1}{2}, \infty) \to R

f (x) = \sqrt{1 + 2 x}, x \in [- \frac{1}{2}, \infty)

lim x \to ⎛ ⎝ \frac{1}{2} ⎞ ⎠ f (x) .

lim x \to \frac{- 1}{2} f (x)

Let f(x) be a polynomial such that $f (- \frac{1}{2})$

=0, then a factor of f(x) is

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