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Find the Radius of curvature for the curve y^2= (a^2 (a-x))/x at the point (a,0)

Find the Radius of curvature for the curve y^2= (a^2 (a-x))/x at the point (a,0) Question Question Find the Radius of curvature for the curve y^2= (a^2 (a-x))/x at the point (a,0) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of…

Find the radius of curvature of the cycloid x=a((theta)+sin(theta)), y=a (1-cos(theta))

Find the radius of curvature of the cycloid x=a((theta)+sin(theta)), y=a (1-cos(theta)) Question Question Find the radius of curvature of the cycloid x=a((theta)+sin(theta)), y=a (1-cos(theta)) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find…

Find the Radius of curvature for the curve y^2= (4a^2 (2a-x))/x where the curve meets the x-axis

Find the Radius of curvature for the curve y^2= (4a^2 (2a-x))/x where the curve meets the x-axis Question Question Find the Radius of curvature for the curve y^2= (4a^2 (2a-x))/x where the curve meets the x-axis Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta)…

Find the radius of curvature of the curve y=a log sec(x/a) at any point (x,y)

Find the radius of curvature of the curve y=a log sec(x/a) at any point (x,y) Question Question Find the radius of curvature of the curve y=a log sec(x/a) at any point (x,y) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of…

For the curve y=ax/ (a+x), Show that (2ρ/a) ^ (2/3)=(x/y)^2+(y/x)^2

For the curve y=ax/ (a+x), Show that (2ρ/a) ^ (2/3)=(x/y)^2+(y/x)^2 Question Question For the curve y=ax/ (a+x), Show that (2ρ/a) ^ (2/3)=(x/y)^2+(y/x)^2 Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find the radius…

Find the radius of curvature of the curve x^2+y^4=2 at the point (1, 1)

Find the radius of curvature of the curve x^2+y^4=2 at the point (1, 1) Question Question Find the radius of curvature of the curve x^2+y^4=2 at the point (1, 1) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of…

Find the radius of curvature at the point (3a/2, 3a/2) on the curve x^3+y^3=3axy

Find the radius of curvature at the point (3a/2, 3a/2) on the curve x^3+y^3=3axy Question Question Find the radius of curvature at the point (3a/2, 3a/2) on the curve x^3+y^3=3axy Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of…

Find the radius of curvature of the curve represented by x=a ((theta)+sin(theta)) and y=a (1-cos(theta))

Find the radius of curvature of the curve represented by x=a ((theta)+sin(theta)) and y=a (1-cos(theta)) Question Question Find the radius of curvature of the curve represented by x=a ((theta)+sin(theta)) and y=a (1-cos(theta)) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of…

Find the radius of curvature for the curve r=a (1+cos(theta))

Find the radius of curvature for the curve r=a (1+cos(theta)) Question Question Find the radius of curvature for the curve r=a (1+cos(theta)) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find the radius…

Find the radius of curvature of the curve r^n=a^n sin(n theta)

Find the radius of curvature of the curve r^n=a^n  sin(n theta) Question Question Find the radius of curvature of the curve r^n=a^n  sin(n theta) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find…

Find the radius of curvature of the curve r^n=a^n cos(n theta)

Find the radius of curvature of the curve r^n=a^n cos(n theta) Question Question Find the radius of curvature of the curve r^n=a^n cos(n theta) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find…

Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3

Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Question Question Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature…

Find the centre of curvature and circle of curvature for the curve sqrt(x)+sqrt(y)=sqrt(a) at (a/4,a/4)

Find the centre of curvature and circle of curvature for the curve sqrt(x)+sqrt(y)=sqrt(a) at (a/4,a/4) Question Question Find the centre of curvature and circle of curvature for the curve sqrt(x)+sqrt(y)=sqrt(a) at (a/4,a/4) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of…

Find the centre of curvature and circle of curvature for the curve y^2=12x at (x, y) = (3, 6)

Find the centre of curvature and circle of curvature for the curve y^2=12x at (x, y) = (3, 6) Question Question Find the centre of curvature and circle of curvature for the curve y^2=12x at (x, y) = (3, 6) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the…

Find the centre of curvature and circle of curvature for the curve xy=c^2 at (c,c)

Find the centre of curvature and circle of curvature for the curve xy=c^2 at (c,c) Question Question Find the centre of curvature and circle of curvature for the curve xy=c^2 at (c,c) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of…

Find the centre of curvature and circle of curvature for the curve y=x+9/x at (3,6)

Find the centre of curvature and circle of curvature for the curve y=x+9/x at (3,6) Question Question Find the centre of curvature and circle of curvature for the curve y=x+9/x at (3,6) Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of…

Radius of curvature, Centre of curvature, Circle of curvature

Radius of curvature Centre of curvature Circle of curvature Topic Radius of curvature, Centre of curvature, Circle of curvature Radius of curvature Show that for the curve r (1-cos(theta)) =2a, the radius of curvature is (2/sqrt(a)). r^(3/2). (or) p^2 varies as r^3 Find the radius of curvature of the curve r^n=a^n cos(n theta) Find the radius of curvature of the curve r^n=a^n sin(n theta) Find the radius of curvature for the curve r=a (1+cos(theta)) Find the radius of curvature of…

Leibnitz’s theorem

Leibnitz’s theorem Leibnitz's theorem, also known as the product rule for differentiation of two functions, is a formula that allows us to find the nth derivative of a product of two functions. Leibnitz's theorem is a powerful tool for calculating higher order derivatives. It can be extended to find the nth derivative of a product of more than two functions, by applying the formula recursively. Leibnitz's theorem has many applications in mathematics and physics, including the study of partial differential…

If y^(1/m)+y^(-1/m)=2x, prove that (x^2-1 )y_(n+2)+(2n+1)x y_(n+1)+(n^2-m^2 ) y_n=0

If y^(1/m)+y^(-1/m)=2x, prove that (x^2-1 )y_(n+2)+(2n+1)x y_(n+1)+(n^2-m^2 ) y_n=0 Question Question If y^(1/m)+y^(-1/m)=2x, prove that (x^2-1 )y_(n+2)+(2n+1)x y_(n+1)+(n^2-m^2 ) y_n=0 Topic Leibnitz’s theorem Problems Find the n th derivative of x^2 e^x Find the n th derivative of x^2 sin^2 x Find the n th derivative of x^2 log 4x Prove that (1-x^2) y_2 – xy_1 = 2 if y = (sin inverse (x))^2, apply Leibnitz’s theorem to find n^th derivative If tan y=x, then prove that (i) (1+x^2) y_2+2xy_1=0…

If x=sint, y=sin(pt), prove that (1-x^2) y_ (n+2)-(2n+1) xy_ (n+1) + (p^2-n^2) y_n=0

If x=sint, y=sin(pt), prove that (1-x^2) y_ (n+2)-(2n+1) xy_ (n+1) + (p^2-n^2) y_n=0. Question Question If x=sint, y=sin(pt), prove that (1-x^2) y_ (n+2)-(2n+1) xy_ (n+1) + (p^2-n^2) y_n=0. Topic Leibnitz’s theorem Problems Find the n th derivative of x^2 e^x Find the n th derivative of x^2 sin^2 x Find the n th derivative of x^2 log 4x Prove that (1-x^2) y_2 – xy_1 = 2 if y = (sin inverse (x))^2, apply Leibnitz’s theorem to find n^th derivative If…