Let f(x)=(x-1/4)+((x-1)3/12)+((x-1)5/20)+((x-1)7/28) ldots ldots ldots ∞ for x ∈(0,2), then f prime((3/2)) is equal to

Question

Let f(x)=(x-1/4)+((x-1)3/12)+((x-1)5/20)+((x-1)7/28) ldots ldots ldots ∞ for x ∈(0,2), then f prime((3/2)) is equal to (A) (1/2) (B) (1/4) (C) (1/5) (D) (1/3)

Tardigrade Admin · Accepted Answer

f(x)=(1/4)((x-1)+((x-1)3/3)+((x-1)5/5)+((x-1)7/7) ldots ldots . . .) = (1/4) ⋅ (1/2) ln ((1+(x-1)/1-(x-1)))=(1/8) ln ((x/2-x)) f prime(x) =(1/4 x(2-x)) ⇒ f prime((3/2))=(1/3)

Q. Let $f (x) = \frac{x - 1}{4} + \frac{( x - 1 ) ^{3}}{12} + \frac{( x - 1 ) ^{5}}{20} + \frac{( x - 1 ) ^{7}}{28} \dots\dots\dots \infty$ for $x \in (0, 2)$ , then $f^{'} (\frac{3}{2})$ is equal to

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{3}$

Q. Let f(x)=4x−1​+12(x−1)3​+20(x−1)5​+28(x−1)7​………∞ for x∈(0,2), then f′(23​) is equal to

21​

41​

51​

31​

f(x)=41​((x−1)+3(x−1)3​+5(x−1)5​+7(x−1)7​……...) =41​⋅21​ln(1−(x−1)1+(x−1)​)=81​ln(2−xx​) f′(x)=4x(2−x)1​⇒f′(23​)=31​

Q. Let $f (x) = \frac{x - 1}{4} + \frac{( x - 1 ) ^{3}}{12} + \frac{( x - 1 ) ^{5}}{20} + \frac{( x - 1 ) ^{7}}{28} \dots\dots\dots \infty$ for $x \in (0, 2)$ , then $f^{'} (\frac{3}{2})$ is equal to

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{3}$