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Show that f(x)=|x| is not differentiabl...

Show that `f(x)=|x|` is not differentiable at `x=0.`

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To show that the function \( f(x) = |x| \) is not differentiable at \( x = 0 \), we will calculate the left-hand limit (LHL) and the right-hand limit (RHL) of the derivative at that point and check if they are equal. ### Step 1: Define the function and the point of interest The function we are considering is: \[ f(x) = |x| \] We want to check the differentiability at \( x = 0 \). ...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Discuss the continuity of the function f(x)={2x-1 if x<2 ...

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  2. Show that the function f(x)={x^2sin(1/x),ifx!=0 0,ifx=0 is differenti...

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  3. Show that f(x)=|x| is not differentiable at x=0.

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  4. Discuss the differentiability of f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a ...

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  5. For what choice of a and b is the function f(x)={x^2,xlt=c and a x+...

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  6. Discuss the differentiability of f(x)=x|x| at x=0

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  7. Show that the function f(x)={ x^2sin(1/x) , when x!=0 and 0 when x=0 }...

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  8. If f(2)=2 and f^(prime)(2)=1, then find (lim)(x->2)(xf(2)-2f(x))/(x-2)

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  9. A function f:R -> R satisfies the equation f(x+y)=f(x)f(y) for all x,y...

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  10. Show that f(x)=|x| is not differentiable at x=0 .

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  11. Show that the function f(x)={x-1\ \ \ ,\ \ \ if\ x<2 2x-3\ \ \ ,\ \ \ ...

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  12. Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is dif...

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  13. Show that f(x)=x^2 is differentiable at x=1 and find f^(prime)(1) .

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  14. Show that the function f(x)=|x+1|+|x-1| for all x in R , is not diffe...

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  15. Discuss the differentiability of f(x)=x|x| at x=0 .

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  16. Show that the function f(x)={xsin1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 0\ \ ...

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  17. Discuss the differentiability of f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a ...

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  18. If f(x) is differentiable at x=a , find (lim)(x->a)(x^2f(a)-a^2\ f(x))...

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  19. For what choice of a and b is the function f(x)={x^2\ \ \ ,\ \ \ xlt=c...

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  20. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

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