. If f(x) = sinx, g(x) = cos x, in interval [a,b]than find value of c by using
appropriate mean value theorem.
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Answer:
f(x)=sinx+cosx in [0,
2
π
]
As we know that all trigonometric functions are continuous and differentiable in their domain.
Thus f(x) is also continuous and differentiable
Thus, the condition of mean value theorem are satisfied.
Hence, there exists atleast one c∈(0,π) such that ,
f
′
(c)=
2
π
−0
[f(
2
π
)−f(0)]
cosc−sinc=
(
2
π
−0)
(sin
2
π
+cos
2
π
)−(sin0+cos0)
cosc−sinc=0
cosc=sinc
⇒c=
4
π
4
π
lies in the given interval.
Hence LMV is verified.
Answer verified by Toppr
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