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Let P be the point on the curve 4x^2+...

Let `P` be the point on the curve `4x^2+\ alpha^2y^2=4a^2,0

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Let P be the point on the curve 4x^(2)+alpha^(2)y^(2)=4a^(2),0

Find the point on the curve 4x^2+a^2y^(2)=4a^(2), 4 lt a^(2) lt 8 that is farthest from the point (0, –2).

Let P and Q be two points on the curves x^2+y^2=2 and (x^2)/8+y^2/4 =1 respectively. Then the minimum value of the length PQ is

Examine whether point (1, 2) lies on the curve 4x^2 - y^2 =0 .

Let A be the point where the curve 5 alpha ^(2) x ^(3) +10 alpha x ^(2)+ x + 2y - 4=0 (alpha in R, alpha ne 0) meets the y-axis, then the equation of tangent to the curve at the point where normal at A meets the curve again, is:

The point on the curve 4x^(2)+a^(2)y^(2)=4a^(2)4

Tangents are drawn from point P on the curve x^(2) - 4y^(2) = 4 to the curve x^(2) + 4y^(2) = 4 touching it in the points Q and R . Prove that the mid -point of QR lies on x^(2)/4 - y^(2) = (x^(2)/4 + y^(2))^(2)

Let (x,y) be a variable point on the curve 4x^(2)+9y^(2)-8x-36y+15=0 then min(x^(2)-2x+y^(2)-4y+5)+max(x^(2)-2x+y^(2)-4y+5)

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let P be the point on the curve 4x^2+\ alpha^2y^2=4a^2,0<alpha^2<8\...

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  2. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

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  3. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

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  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

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  5. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

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  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|} has a local minimum or a loca...

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  7. A rectagular sheet of fixed permeter with sides having thir lengths in...

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  8. A vertical line passing through the point (h, 0) intersects the ellips...

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  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  10. e total number of local maxima and local minima of the function f(x) =...

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  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

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  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

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  13. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

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  14. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

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  15. The length of a longest interval in which the function 3sinx-4sin^(3...

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  16. If f(x)=e^(1-x) then f(x) is

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  17. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

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  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

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  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

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  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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