Home
Class 12
MATHS
Show that the function f(x)=|sinx+cosx| ...

Show that the function `f(x)=|sinx+cosx|` is continuous at `x=pi` .

Text Solution

Verified by Experts

The correct Answer is:
N/a
We have, `f(x) = |sinx + cosx|` at `x = pi`
Let `g(x) = sinx + cos x`
and ` h(x) = |x|`
` :. hog(x) = h[h(x)]`
`= h (sinx + cosx)`
`= |sinx + cos x|`
Since, `g(x) = sinx + cosx` is a continuous function as it is forming with addition of two continous functions `sinx` and `cosx`.
Also, ` h(x) = |x|` is also a continous function. Since, we know that composite function of two continuous functions is also a continuous function.
Hence, `f(x) = |sinx + cos x|` is a continuous function everywhere.
So, `f(x)` is continuous at `x = pi`.
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR|Exercise Application Of Integrals|68 Videos

  • DETERMINANTS

    NCERT EXEMPLAR|Exercise Determinants|58 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x)=2x-|x| is continuous at x=0 .

Show that the function f(x)=2x-|x| is continuous at x=0.

Show that the function f(x)=2x-|x| is continuous at x=0

Show that the function defined by f(x)=|cos x| is a continuous function.

Show that the function f(x)=|x-2| is continuous but not differentiable at x=2.

Show that the function defined by f(x)=sin(x^(2)) is a continuous function.

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

Show that the function defined by f(x)=cos(x^(2)) is a continuous function.

The period of the function f(x)=|sinx|-|cosx| , is