can anyone solve the problem
Answers
sin(a+1)x+ sinx if x<0
Let fix)=
, if x>0
bx√x Since f(x) is continuous at x = 0, we have
lim f(x)=f(0) = lim f(x)
Let us consider the left hand limit: lim f(x)= lim sin(a+1)x+sinx
1414
sinaxxcosx +cosaxxsinx+sinx = lim 240 sinax:xcosx cosax xsinx
X-D X sinax = Ilm xlim cosx +Ilm cosaxx lim+lim
sinx
= lim
+ lim
+ lim lim. sinx
sinx
sinax
sinx
5 nx
x1+ 1x lim
+ lim
lim
sinax sinx sinx - lim xa+ limi lim + lim: ax X X
lim cosx=1, Imcosa=11
sinax
sinx
sinx
=alim. +lim,
+ lim+lim
X ax
X-0 X
=ax 1+1+1
sinax
sinx
= 1; lim
-=
xo ax
240 X
= lim
= a + 2
Let us consider the right hand limit: lim fix) lim
bx√√x
√√√x+bx² =√x √√x+bx² + √x
x+bx²-x = lim
• bx√x [√x +Dx² + √x] bx²
- lim
= lim x=0 √x [√x+bx² + √x] √x x+0 [√x+bx² +√√x]
=lim √x √x x-0 (√√x+bx² + √√x • ( √x √x )
- lim
1
x=0 (√1+bx+√I)
1
2
f(0) = lim f(x) = c
= lim
Since the function is continuous lim f(x)=f(0) = lim f(x) 1405
