Let f(x)=⎩⎨⎧n→∞lim(4cot(πx))n+1ax(x−1)(4cot(πx))n+(px2+2),x∈(0,1)∪(1,2)and0,x=1 If f(x) is differentiable for all x∈(0,2) then (a2+p2) equals

Click here to view the solution.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Let {f{{({x})}}}={_{{{n}}}{{{a}{x}{({x}-{1})}{({{{{({x})}}}}{{

Question

Let $f (x) = ⎩ ⎨ ⎧ n \to \infty lim \frac{a x ( x - 1 ) ( \frac{c o t ( π x )}{4} ) ^{n} + ( p x ^{2} + 2 )}{( \frac{c o t ( π x )}{4} ) ^{n} + 1}, x \in (0, 1) \cup (1, 2) and 0, x = 1$ If f(x) is differentiable for all $x \in (0, 2)$ then $(a^{2} + p^{2})$ equals

Views: 732 students

Found 8 tutors discussing this question

Camila Discussed

Let

f (x) = ⎩ ⎨ ⎧ n \to \infty lim \frac{a x ( x - 1 ) ( \frac{c o t ( π x )}{4} ) ^{n} + ( p x ^{2} + 2 )}{( \frac{c o t ( π x )}{4} ) ^{n} + 1}, x \in (0, 1) \cup (1, 2) and 0, x = 1

If f(x) is differentiable for all

x \in (0, 2)

then

(a^{2} + p^{2})

equals

8 mins ago

Discuss this question LIVE

8 mins ago

Question Text

Let

f (x) = ⎩ ⎨ ⎧ n \to \infty lim \frac{a x ( x - 1 ) ( \frac{c o t ( π x )}{4} ) ^{n} + ( p x ^{2} + 2 )}{( \frac{c o t ( π x )}{4} ) ^{n} + 1}, x \in (0, 1) \cup (1, 2) and 0, x = 1

If f(x) is differentiable for all

x \in (0, 2)

then

(a^{2} + p^{2})

equals