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Show that f(x)=|x-3| is continuous but n...

Show that `f(x)=|x-3|` is continuous but not differentiable at `x=3` .

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To show that the function \( f(x) = |x - 3| \) is continuous but not differentiable at \( x = 3 \), we will follow these steps: ### Step 1: Check Continuity at \( x = 3 \) A function is continuous at a point if the left-hand limit (LHL), right-hand limit (RHL), and the function's value at that point are all equal. 1. **Calculate the Left-Hand Limit (LHL)**: \[ ...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

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  2. A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all ...

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  3. Show that f(x)=|x-3| is continuous but not differentiable at x=3 .

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  4. Show that f(x)=x^(1//3) is not differentiable at x=0 .

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  5. Show that f(x)={12 x-13 ,\ \ \ if\ xlt=3 2x^2+5,\ \ \ \ \ if\ x >3 is ...

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  6. Show that the function f defined as follows f(x)={3x-2,\ \ \ \ 0<xlt=1...

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  7. Discuss the continuity and differentiability of the function f(x)=|...

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  8. Find whether the following function is differentiable at x = 1 and ...

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  9. Show that the function f(x)={x^msin(1/x), 0 ,\ \ \ x!=0 ,\ \ \ \ \ \...

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  10. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \ ...

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  11. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \ ...

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  12. Find the values of a and b so that the function f(x)={x^2+3x+a ,\ \ if...

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  13. Show that the function f(x)={|2x-3|\ [x],\ \ \ xgeq1sin((pix)/2),\ \ \...

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  14. If f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ ...

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  15. Find the values of a and b , if the function f(x) defined by f(x)={x^2...

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  16. If f(x)=x^2+2x+7 , find f\ '\ (3) .

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  17. Find f\ '\ (2) and f\ '\ (5) when f(x)=x^2+7x+4 .

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  18. For the function f given by f(x)=x^2-6x+8 , prove that f\ '\ (5)-3\ f\...

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  19. Discuss the continuity and differentiability of f(x)={1-x ,\ \ \ \ ...

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  20. Discuss the differentiability of f(x)=|x-1|+|x-2|

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