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A polynomial function f(x) satisfies the...

A polynomial function `f(x)` satisfies the condition `f(x+1)=f(x) + 2x + 1`. Find `f(x)` if `f(0)=1` Findalso the equations of the pair of tangents from the origin on the curve `y =f(x)` and compute the areaenclosed by the curve and the pair of tangents.

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The correct Answer is:
`f(x) = x^(2) + 1; y = pm 2x ; A = 2/3` sq. units
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MOTION-AREA UNDER THE CURVE-EXERCISE -3
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  10. A polynomial function f(x) satisfies the condition f(x+1)=f(x) + 2x + ...

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  11. Find the equation of the line passing through the origin and dividing ...

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  12. Consider the curve y=x^n where n > 1 in the 1^st quadrant. Ifthe areab...

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  13. In the adjacent figure the graph of two function y=f(x) and y=sin x ar...

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  14. If An be the area bounded by the curve y=(tanx^n) ands the lines x=0,\...

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  15. Find the whole area included between the curve x^2)y^(2) = a^(2)(y^(2)...

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  16. Let C(1 )and C(2) be two curves passing through the origin as shown in...

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  17. Consider the two curves y = 1//x^(2) and y = 1//[4(x-1)]. At what v...

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  18. If A = [[ln(a-1),0],[0,ln(b-1)]], then A^(-1) is :

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  19. If z is a complex number such that z = ln(a – 1) + iln (b – 1) then ar...

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  20. {:(,"Column - I", "Column - II"),("(A)" ,"The area bounded by curve","...

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