If f(x)= (2x-3sinx)/(3x+4tanx ) ;x≠0 ,is continuous at x=0 ,then f(0) is
(A)-2/7 (B) 2/7 (C) -1/7 (D) 3/7
Answers
Answered by
0
Answer:
Given,
f(x)=
3x+2sinx
2x+3sinx
If f(x) is continuous at x=0, then
x→0
llim
f(x)=f(0)
x→0
lim
3x+2sinx
2x+3sinx
=f(x)
⇒f(0)=
x→0
lim
x(3+
x
2sinx
)
x(2+
x
3sinx
)
⇒f(0)=
x→0
lim
(3+
x
2sinx
)
(2+
x
3sinx
)
⇒f(0)=
x→0
lim
(3+
x
2sinx
)
x→0
lim
(2+
x
3sinx
)
⇒f(0)=
3+2
x→0
lim
(
x
sinx
)
2+3
x→0
lim
(
x
sinx
)
⇒f(0)=
3+2⋅1
2+3⋅1
⇒f(0)=
5
5
=1
Answered by
1
Answer:
divide both numerator and denominator by x
We get
2-3sinx/x
_______. •°• we know sinx / x = 1
3+4tanx/x. •°• we know tanx / x =1
•°•2-3
____ = -1/7
3+4
CORRECT OPTION IS C
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