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Discuss the continuity of the followi...

Discuss the continuity of the following function at x = 0 : `"f"("x")={("x"^4+2x^3+x^2)/(tan^(-1)x),x!=0 and 0,x=0}`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
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  2. Verify Lagranges mean value theorem for the following function: "...

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  3. Discuss the continuity of the following function at x = 0 : "f"("...

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  4. Solve the following differential equation: "x"("dy")/("dx")+"y"="x"lo...

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  5. Show that: int0^(pi/2) "sqrt(tanx) +sqrt(cotx)=sqrt(2)pi

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  6. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right ang...

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  7. Using properties of determinants, prove that following |(a+b+2c,a,b),(...

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  8. If |[x+2, 3],[x+5, 4]|=3 , find the value of x

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  9. Show that the points (1,0), (6,0), (0,0) are collinear.

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  10. If "f"("x")=sqrt((sec"x"-1)/(secx+1))" " find "f '"("x")dot Also fin...

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  11. If xsqrt(1+y)+ysqrt(1+x)=0, find ("dy")/("dx") . To prove (dy)/(dx)=...

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  12. Show that the semi vertical angle of a right circular cone of given ...

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  13. If the equation of a line "A B" is ("x"-3)/1=("y"+2)/(-2)=("z"-5)/4...

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  14. If "f"("x") is an invertible function, find the inverse of "f"("x")...

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  15. If [[(x+3y),y],[7-x,4]]=[(4,-1),(0,1)], find the values of x and y.

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  16. Solve for x: tan^-1((1-x)/(1+x))=1/2 tan^-1 x, x > 0

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  17. Evaluate: int("x"+cos6"x")/(3"x"^2+sin6"x")" dx"

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  18. If int("e"^("a x")+"bx")"dx"=1/4"e"^(4"x")+(3"x"^2)/2" find the values...

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  19. A and B throw a pair of die turn by turn. The first to throw 9 is a...

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  20. Find the equation of the line passing through the point "P"(4,6,2) ...

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