Mathematics Problems

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 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) 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) 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) 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) 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…

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. 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…

If y=cos(mlog x), prove that x^2 y_(n+2)+(2n+1)xy_(n+1)+(m^2+n^2 ) y_n=0. Question Question If y=cos(mlog x), prove that x^2 y_(n+2)+(2n+1)xy_(n+1)+(m^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 tan y=x, then prove that (i) (1+x^2) y_2+2xy_1=0…

If sin^(-1)y=2 log(x+1), prove that (x+1)^2 y_(n+2)+(2n+1)(x+1) y_(n+1)+(n^2+4) y_n=0. Question Question If sin^(-1)y=2 log(x+1), prove that (x+1)^2 y_(n+2)+(2n+1)(x+1) y_(n+1)+(n^2+4) 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 y=(x+sqrt(x^2-1))^m, prove that (x^2-1) y_(n+2)+(2n+1)xy_(n+1)+(n^2-m^2 ) y_n=0. Question Question If y=(x+sqrt(x^2-1))^m, prove that (x^2-1) y_(n+2)+(2n+1)xy_(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 (ii) (1+x^2)…

If y=sin(log(x^2+2x+1)), prove that (x+1)^2 y_(n+2)+(2n+1)(x+1) y_(n+1)+(n^2+4 )y_n=0. Question Question If y=sin(log(x^2+2x+1)), prove that (x+1)^2 y_(n+2)+(2n+1)(x+1) y_(n+1)+(n^2+4 )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 (ii) (1+x^2)…

If x = tan(log y), find the value of (1+x^2) y_ (n+1) + (2nx-1)y_n + n (n-1) y_ (n-1). Question Question If x = tan(log y), find the value of (1+x^2) y_ (n+1) + (2nx-1)y_n + n (n-1) y_ (n-1). 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…

If tan y=x, then prove that (i) (1+x^2) y_2+2xy_1=0 (ii) (1+x^2) y_ (n+2) +2(n+1) xy_ (n+1) +n (n+1) y_n=0 Question Question If tan y=x, then prove that (i) (1+x^2) y_2+2xy_1=0 (ii) (1+x^2) y_ (n+2) +2(n+1) xy_ (n+1) +n (n+1) 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…

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. Question Question 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. 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…

Find the n th derivative of x^2 log 4x. Question Question Find the n th derivative of x^2 log 4x. 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…

Find the n th derivative of x^2 sin^2 x. Question Question Find the n th derivative of x^2 sin^2 x. 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…

Find the n th derivative of x^2 e^x. Question Question Find the n th derivative of x^2 e^x. 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 (ii) (1+x^2)…

Find the pedal equation of 2a/r=1-cos(theta). Question Question Find the pedal equation of 2a/r=1-cos(theta). Topic Pedal equation of a polar curve Problems Find the pedal equation of the curve r^m=a^m (cosm(theta)+sinm(theta)). Find the pedal equation of 2a/r=1+cos(theta) Obtain the pedal equation of the curve r^n=a^n cos(n theta) Find the pedal equation of r^n=a (1+cos(n theta)) Find pedal equation of the curve r=a e^ ((theta)cot(alpha)) Find the pedal equation of 2a/r=1-cos(theta)  

Find pedal equation of the curve r=a e^ ((theta)cot(alpha)). Question Question Find pedal equation of the curve r=a e^ ((theta)cot(alpha)). Topic Pedal equation of a polar curve Problems Find the pedal equation of the curve r^m=a^m (cosm(theta)+sinm(theta)). Find the pedal equation of 2a/r=1+cos(theta) Obtain the pedal equation of the curve r^n=a^n cos(n theta) Find the pedal equation of r^n=a (1+cos(n theta)) Find pedal equation of the curve r=a e^ ((theta)cot(alpha)) Find the pedal equation of 2a/r=1-cos(theta)