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Find the equation of the tangent to the ...

Find the equation of the tangent to the curve `x = y^2-1` at the point where the slope of the normal to the curve is 2.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the number of critical points of f(x)=frac[abs(x-1)][x^2]

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  2. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  3. Find the equation of the tangent to the curve x = y^2-1 at the point w...

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  4. If y=sin^(-1)(x^3), then find that dy/dx

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  5. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

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  6. Evaluate int0^2abs(x^2+2x-3)dx

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  7. Find the area of the region bounded by the curve y=sin^(3)x and the st...

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  8. intdx/(1+tanx)

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  9. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

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  10. Find the solution of the following differential equations: (4x+6y+5)dx...

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  11. Let veca,vecb,vecc be three vectors such that veca+vecb+vecc=vec0 and ...

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  12. Find the image of the point (2,-1,3) in the plane 3x-2y+z-9=0

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  13. Find the co-ordinates of the foot of the perpendicular from the point ...

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  14. Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors para...

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  15. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  16. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  17. Show that the sum of the intercepts on the coordinate axes of any tang...

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  18. Find frac[dy][dx] if y=([sinx+x^2]/[cot2x]).

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  19. Integrate intfrac[(sin^2x+cos2x)][cos^2x)]dx

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  20. Solve the following differential equations (x+tany)dy= sin 2y ""dx

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