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If f(4)=4, f'(4)=1, then find lim(xrarr4...

If `f(4)=4`, `f'(4)=1`, then find `lim_(xrarr4)(2-sqrtf(x))/(2-sqrtx)`

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USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
  1. If f(x+y)=f(x)f(y) for all x,yinR and f(5)=4 and f'(0)=2, then find f'...

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  2. If f(x)=abs(cos 2x), then find f'(pi/4+0)

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  3. If f(4)=4, f'(4)=1, then find lim(xrarr4)(2-sqrtf(x))/(2-sqrtx)

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  4. Find the values of x, for which d/dxcot(cot^-1x)=1.

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  5. Find x, for which d/dx cos(cos^-1 x)=1.

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  6. Write the value x for which d/dxsin^-1(sin x)=1

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  7. Find x, for which d/dx cos(cos^-1 x)=1.

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  8. Find x, for which d/dxsec(sec^-1x)=1.

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  9. If y=sin^-1x and z=2cos^-1x, find dy/dz.

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  10. If y=t^2 and x=t^3 find, dy/dx at t=1.

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  11. If x=log t, y=sin t, find dy/dx at t=pi/2. State true or false in exer...

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  12. Differential coefficient of sin^-1((2x^3)/(1+x^6)) with respect to x i...

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  13. There is no function which is its own derivative

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  14. The derivative of a non constant even function is always an odd functi...

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  15. If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1/(sqrt(t^2+1))) then dy/dx is ...

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  16. The derivative of sec^-1(1/(2x^2-1)) w.r.t. sqrt(1-x^2) is 3

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  17. Derivative of log10sinx w.r.to x is cotx.log10e

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

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  19. f(x)=xabsx is derivable at x=0.

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  20. Fill in the blanks : The derivative of sec^-1x w.r.to x if xlt-1 is

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