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If f'(c) is the -derivative of f(x) at x= c,then show that `lim_(xrarrc)(xf(c)-cf(x))/(x-c)=f(c)-cf'(c)`

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 7-EXERCISE
  1. Find the co-ordinate of the point which is equidistance from (alpha, 0...

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  2. Calcualte the angle between the straight linesx+sqrt3 y+2=0and y+5=0

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  3. If f'(c) is the -derivative of f(x) at x= c,then show that lim(xrarrc...

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  4. Evaluate :lim(xrarr3)(x^2-9)/(sqrt(x-2)-sqrt(4-x))

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  5. 4 cards are drawn from a well - shuffled deck of 52 cards. What is the...

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  6. If the variance of a distribution is 4 coefficient of variation is 5%,...

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  7. If f(x)=cos(logx),show that f(x)f(y)-1/2[f(x/y)+f(xy)]=0

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  8. Prove that cosalpha/(sin3alpha)+(cos3alpha)/(sin9alpha)+(cos9alpha)/(s...

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  9. Solve : sectheta-1=(sqrt2-1)tantheta

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  10. By mathematical induction show that 3^n>n^3when nge4. N is an integer.

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  11. Find the co-efficient of 1/xof the expansion of (1+x)^n(1+1/x)^nwhere ...

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  12. Find the sum up to n terms :n.1+(n-1).2+(n-2)3+(n-3).4+....

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  13. If n(p(r-1))/a=n(pr)/b=n(p(r+1))/c,then show that b^2=a(b+c)

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  14. Show that the four lines 2x+y+1=0,2x+y+7=0,x+2y-1=0 and x+2y+5=0 form ...

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  15. Find the equation-of the bisector of the obtused angle between the st...

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  16. The co-ordinate of centre and the diameter of a circle are (3, 7) and ...

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  17. Find the ratio in which the YZ. plane divides the line segment joining...

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  18. Evaluate :lim(xrarr0)(sqrtcosx-root(3)(cosx))/(sin^2x)

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  19. Find, form 1st principles, the derivatives of tansqrtxwith respect to ...

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  20. Using contrapositive method show that the following statement is true....

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