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If y=sqrt(x+1)+sqrt(x-1), prove that sqr...

If `y=sqrt(x+1)+sqrt(x-1)`, prove that `sqrt(x^2-1)(dy)/(dx)=1/2y`.

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PRADEEP PUBLICATION-MODEL PAPER (2)-EXERCISE
  1. Let f(x)={(xsin(1/x), x ne 0),(k, x=0):} find k if f is continuous at ...

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  2. Evaluate underset(xrarr0)Lt [cosx] if it exists. Here [] denotes the g...

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  3. If y=sqrt(x+1)+sqrt(x-1), prove that sqrt(x^2-1)(dy)/(dx)=1/2y.

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  4. Evaluate underset(-1)overset1 int 1/(1+e^x)dx.

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  5. Find the equation of the plane given that the foot of perpendicular d...

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  6. Find the transpose of {:[(a,b),(c,d)]

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  7. Evaluate: underset0overset(pi//2)int log(sinx)dx

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  8. Let S be the set of all real numbers except 1 and 'o' be an operation ...

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  9. Let A=Set of all real numbes except 1. Let * be defined as a+b-ab for...

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  10. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  11. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  12. Prove that cot^-1 7 + cot^-1 8 + cot^-1 18 = cot^-1 3

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  13. Solve the following equations sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1

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  14. Solve the following equations 5x-7y+z=11, 6x-8y-z=15, 3x+2y-6z=7 by Cr...

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  15. Find dy/dx if x^y + y^x = a^b

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  16. If f(x)={((x-5)/(|x-5|)+a" , if "xlt5),(a+b" , if "x=5),((x-...

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  17. Find the interval of increase and decrease of the function f(x)=log(1+...

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  18. Prove that the curves x=y^2 and xy=k cut at right angles* if 8k^2 =1

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  19. int (sin^-1x)/(1-x^2)^(3//2) dx

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  20. Evaluate: underset0 oversetpi int sinxdx .

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