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If y = (x-1)log(x-1)-(x+1)log(x+1), prov...

If `y = (x-1)log(x-1)-(x+1)log(x+1)`, prove that : `dy/dx = log((x-1)/(1+x))`

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. The function f(x)=e^(-|x|) is continuous everywhere but not differenti...

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

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  3. If y = (x-1)log(x-1)-(x+1)log(x+1), prove that : dy/dx = log((x-1)/(1+...

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

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

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  6. Let f(x)={1/(|x|)for|x|geq1a x^2+bfor|x|<1iff(x) is continuous and dif...

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  7. If f(x) = sqrt(1-(sqrt1-x^2)) , then f(x) is (a)continuous on [-1, ...

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  8. If f(x)=a|sinx|+be^|x|+c|x|^3 and if f(x) is differentiable at x=0 the...

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  9. Solve the following equation for x : cos(tan^-1 x) = sin(cot^-1(3/4))

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  10. Find the principal values the following : sin^-1{cos(sin^-1(sqrt(3)/2)...

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  11. Solve the following equation for x : cos(tan^-1 x) = sin(cot^-1(3/4))

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  12. For the principal values, evaluate the following : sin^-1(-sqrt(3)/2)+...

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  13. If A is a square matrix such that |A| = 2, write the value of | AA^T|

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  14. Find the domain of the function f(x) = sin^-1 sqrt(x-1)

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  15. If sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2, then find the value of x^2+y^2+...

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  16. If f(x) = (x^l/x^m)^(l+m) (x^m/x^n)^(m+n) (x^n/x^l)^(n+l), then find f...

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

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  18. Evaluate : tan(cos^-1(-7/25))

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

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

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