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If the derivatives of f(x) at x=a is f'(...

If the derivatives of f(x) at x=a is f'(a) ,then show that `lim_(xrarra)(xf(a)-af(x))/(x-a)=f(a)-af'(a)`

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If the derivative of f(x) at x = a be f'(a) show that lim_(x to a ) (xf(a)-af(x))/(x-a) = f(a) -af'(a) .

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If a function f(x) is derivable at x = a, then show that underset(x rarr a)lim (x^(2)f(a) - a^(2)f(x))/(2(x-a)) = af(a) - 1/2(a^(2)f'(a))

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 2-EXERCISE
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  2. The co-efficients of the expansion of (1+x)^(2n-1)and (1+x)^(2n)are P ...

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  3. The co-ordinates of the vertices of a quadrilateral are (3,-2)(6,2)(4,...

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  4. Find the equations of straight line which are perpendicular to the str...

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  5. A circle through the common points of the circles x^2+y^2-x+7y-3=0and ...

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  6. Find the equations of the two straight line parallel to the line 3x+4y...

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  7. Evaluate :lim(xrarr0)((a+x)^2sin(a+x)-a^2sina)/pi

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  8. If the derivatives of f(x) at x=a is f'(a) ,then show that lim(xrarra)...

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  9. If n is a such real number that n>3 .then n^2>9 prove it by the method...

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  10. From 20 cards marked with the 1st 20 natural numbers.one is drawn at r...

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  11. Find the mean of first ten natural numbers

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  12. If tan (theta/2)=tan^3 (phi/2)and tanphi=2tanalpha,then prove that the...

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  13. Find the value of 1/2sec80^@-2cos20^@

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  14. Find the common solution region by graphical method.2x + y ge 2, x - y...

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  15. Solve.sqrt3x^2-sqrt2x+3sqrt3=0

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  16. Find the sum to n terms :1/2+3/2^2+5/2^3+...+(2n-1)/2^n

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  17. If the sum of the first m terms of an A.P. is equal to the sum of eith...

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  18. PQ is a double ordinate of the parabolay^2=4axShow that thelocus of it...

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  19. Show that for all values of t the point x=c((1+t^2)/(1-t^2)),y=(2ct)/(...

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  20. The eccentric angles of the two points P and Q on the ellipsex^2/a^2+y...

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