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The function f(x) =sin|x| is continuous ...

The function `f(x) =sin|x|` is continuous for all x

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To prove that the function \( f(x) = \sin |x| \) is continuous for all \( x \), we can follow these steps: ### Step 1: Identify the Functions Let \( g(x) = \sin x \) and \( h(x) = |x| \). The function \( f(x) \) can be expressed as the composition of these two functions: \[ f(x) = g(h(x)) = \sin(|x|) \] ...
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NCERT ENGLISH-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5.1
  1. Find the relationship between a and b so that the function f defined ...

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  2. Discuss the continuity of the function f, where f is defined byf(x)={...

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  3. Is the function defined by f(x)={{:(x+5, ifxlt=1),(x-5, ifx >1):} a c...

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  4. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  5. Find all points of discontinuity of f, where f is defined byf(x)={{:(...

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  6. Find the values of k so that the function f is continuous at the indi...

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  7. Find the values of k so that the function f is continuous at the indi...

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  8. Find all points of discontinuity of f, wheref(x)={{:((sinx)/x , ifx<0)...

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  9. Discuss the continuity of the cosine, cosecant, secant and cotangent ...

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  10. Discuss the continuity of the following functions: (a) f(x) = sin x + ...

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  11. Is the function defined by f(x)=x^2-sinx+5 continuous at x=pi?

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  12. Find the values of k so that the function f is continuous at the indi...

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  13. Find the values of k so that the function f is continuous at the indi...

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  14. Examine the continuity of f, where f is defined byf(x)={{:(sinx-cosx ,...

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  15. Determine if f defined by f(x)={{:(x^2 sin(1/x) , ifx!=0),( 0, ifx=0):...

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  16. Find all the points of discontinuity of f defined by f(x) = | x | - |...

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  17. Find the values of a and b such that the function defined by f(x)={{:...

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

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

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  20. The function f(x) =sin|x| is continuous for all x

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