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If 'f(x)= {((1-cos4x)/(x^2)),whenx<0),(k...

If 'f(x)= {((1-cos4x)/(x^2)),whenx<0),(k,whenx=0),(sqrtx/(sqrt(16+sqrtx))-4) ,when x>0):}`, and f is continuous at x=0, then find the value of k.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. Show that : sin^2x is continuous for everyreal value of x.

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  2. f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

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  3. If 'f(x)= {((1-cos4x)/(x^2)),whenx<0),(k,whenx=0),(sqrtx/(sqrt(16+sqrt...

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  4. Find the value of k so that the function f defined by f(x)={((kcos x)/...

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  5. If the function f(x)={:{(3ax+b", if "xgt1),(11", if "x=1)...

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

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  7. Find the derivative of tan^(-1)((cosx+sinx)/(cosx-sinx)) w.r.t. x.

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  8. What is the derivative of e^(3logx) w.r.t.x?

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  9. If u=t^2and v=sint^2then dv/du=.

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  10. If y=sec^(-1)(sqrtx+1)/sqrtx+sin^(-1)fracsqrtx(sqrtx+1)then dy/dx=

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  11. Write the derivative of sinx with respect to cosx.

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  12. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))] then find (dy)/(dx)

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  13. if e^x+e^y=e^(x+y) then show that (dy)/(dx)+e^(y-x)=0.

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  14. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  15. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  16. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t sin^(-1)((2x)/(1+x^2))...

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  17. Write that condition of Rolle’s theorem which is violated by the funct...

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  18. If f(0)=0,f'(0)=2 then what is the derivative of y = f(f(f(f(x)))) at...

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  19. If y = tan^(-1)(1/(1+x+x^2)) + tan^(-1)(1/(x^2+3x+3)) + tan^(-1)(1/(x^...

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  20. If x=a(cos t + log tan (t/2)),y=a sin t, then what is (d^2y)/(dx^2) at...

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