Q21 If f(x)=2cosx-1cotx-1∀x∈0, π2 except at x=π4 Define fπ4 so that f(x) may be continuous at x=π4 - Maths - Continuity and Differentiability

Question

Q21 If f ( x ) = 2 cos x - 1 c o t x - 1 ∀ x ∈ 0 ,
  π 2 except at x = π 4 Define f π 4 so that
f(x) may be continuous at x = π 4 Ans: 1 2

Aarushi Mishra · Accepted Answer

Dear studentThe question is a little wrong
 It should befx=2cos x -1cot x -1For fx to be continuous at x=π4limx→π4 fx=fπ4fπ4=limx→π4 fx=limx→π4 2cos x -1cot x -1It is 0/0 form Use L-Hospital rule=limx→π4 d dx2cos x -1d dxcot x -1=limx→π4 -2sin x-cosec2 x=limx→π4 2sin xcosec2 x= 2sin π4cosec2 π4=2×1222=12

Q21. If f ( x ) = 2 cos x - 1 c o t x - 1 ∀ x ∈ 0 , π 2 except at x = π 4 . Define f π 4 so that f(x) may be continuous at x = π 4 . Ans: 1 2

Q21. If $f (x) = \frac{\sqrt{2} \cos (x - 1)}{c o t (x - 1)} \forall x \in (0, \frac{π}{2})$ except at $x = \frac{π}{4}$ . Define $f (\frac{π}{4})$ so that f(x) may be continuous at $x = \frac{π}{4}$ . Ans: $\frac{1}{2}$