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Write the value of the derivative of `f(x)=|x-1|+|x-3|` at `x=2` .

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To find the value of the derivative of the function \( f(x) = |x - 1| + |x - 3| \) at \( x = 2 \), we can follow these steps: ### Step 1: Identify the function and the point of interest The function is \( f(x) = |x - 1| + |x - 3| \), and we need to find \( f'(2) \). ### Step 2: Use the definition of the derivative The derivative \( f'(x) \) can be calculated using the limit definition: \[ ...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Write the number of points where f(x)=|x|+|x-1| is continuous but n...

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  2. If (lim)(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of...

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  3. Write the value of the derivative of f(x)=|x-1|+|x-3| at x=2 .

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  4. If f(x)=sqrt(x^2+9) , write the value of (lim)(x->4)(f(x)-f(4))/(x-4) ...

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  5. Let f(x)=|x| and g(x)=|x^3| , then f(x) and g(x) both are continuous a...

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  6. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

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  7. The set of points where the function f(x)=x|x| is differentiable i...

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  8. If f(x)={(|x+2|)/(tan^(-1)(x+2)),\ \ \ x!=-2 2,\ \ \ \ \ \ \ \ \ \ \ \...

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  9. Let f(x)=|x| . Then, for all x f is continuous (b) f is differentiabl...

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  10. The function f(x)=e^(|x|) is (a) Continuous everywhere but not differ...

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  11. The function f(x)=|cosx| is (a) everywhere continuous and differe...

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  12. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1...

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  13. If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and if f(x) is differentiable at x...

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  14. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)++(x^2)/((1+x^2)^n)+ , then...

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  15. If f(x)=|(log)e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'...

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  16. If f(x)=|(log)e|x| , then f(x) is continuous and differentiable for...

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  17. Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is c...

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  18. The function f(x)=x-[x] , where [] denotes the greatest integer fun...

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  19. Let f(x)={a x^2+1,\ \ \ \ \ x &gt;1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 ...

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  20. Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. ...

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