Mathematics Problems

if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1 Question Solution Question if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1   Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1   Type 2 Questions if…

if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 Question Solution Question if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0   Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1   Type 2 Questions if…

if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu Question Solution Question if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu   Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1   Type 2 Questions if x^x y^y z^z=c show…

if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) Question Solution Question if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y)   Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1  …

if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 Problem Solution Problem if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1   Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1   Type 2 Questions if x^x y^y z^z=c show thatn (∂^2…

if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 Problem Solution Problem if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0   Type 1 Questions if u=x^3-3xy^2+x+(e^x cosy)+1, show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))=0 if u= log((x^2+y^2)/(x+y)), show that xu_x+yu_y=1 if u=tan^(-1)(y/x), verify that (∂^2 u)/(∂y ∂x) = (∂^2 u)/(∂x ∂y) if u=e^(ax+by)f(ax-by), prove that (b ∂u/∂x)+(a ∂u/∂y)=2abu if u=1/√(x^2+y^2+z^2), then show that ((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2))=0 if u=log√(x^2+y^2+z^2), then show that (x^2+y^2+z^2)(((∂^2 u)/(∂x^2))+((∂^2 u)/(∂y^2))+((∂^2 u)/(∂z^2)))=1   Type 2 Questions if x^x y^y…

Evaluate lim(x→0) [(sin^2(π/(2-x))]^sec^2(π/(2-x)) Problem Solution Problem Evaluate lim(x→0) [(sin^2(π/(2-x))]^sec^2(π/(2-x)) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x - x)/(x ^ 2 * tan…

Evaluate lim(x→0) ((a^x+b^x+c^x+d^x)/4)^(1/x) Problem Solution Problem Evaluate lim(x→0) ((a^x+b^x+c^x+d^x)/4)^(1/x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x - x)/(x ^ 2 * tan…

Evaluate lim(x→0) ((a^x+b^x+c^x)/3)^(1/x) Problem Solution Problem Evaluate lim(x→0) ((a^x+b^x+c^x)/3)^(1/x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x - x)/(x ^ 2 * tan…

Evaluate lim(x→0) ((a^x+b^x)/2)^(1/x) Problem Solution Problem Evaluate lim(x→0) ((a^x+b^x)/2)^(1/x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x - x)/(x ^ 2 * tan…

Evaluate lim(x→0) (tanx/x)^(1/x) Problem Solution Problem Evaluate lim(x→0) (tanx/x)^(1/x) Evaluate lim(x->0) (tanx/x)^(1/x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x - x)/(x ^…

Evaluate lim(x→π/2)⁡ (sin⁡x )^(tan⁡x) Evaluate lim(x->pi/2)⁡ (sin⁡x )^(tan⁡x) Problem Solution Problem Evaluate lim(x→π/2)⁡ (sin⁡x )^(tan⁡x) Evaluate lim(x->π/2)⁡ (sin⁡x )^(tan⁡x) Evaluate lim(x→pi/2)⁡ (sin⁡x )^(tan⁡x) Evaluate lim(x->pi/2)⁡ (sin⁡x )^(tan⁡x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x…

Evaluate lim (x->0) ( (1 + sinx - cosx + log(1-x)) / (x tan^2 x) ) Problem Solution Problem Evaluate lim (x->0) ( (1 + sinx - cosx + log(1-x)) / (x tan^2 x) ) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0)…

Evaluate lim (x->0) ((e^x - e^(-x) - 2 log(1+x)) / (x sinx) ) Problem Solution Problem Evaluate lim (x->0) ((e^x - e^(-x) - 2 log(1+x)) / (x sinx) ) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim…

Evaluate lim (x->0) ((1/x^2)-(cot^2 x)) Problem Solution Problem Evaluate lim (x->0) ((1/x^2)-(cot^2 x)) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x - x)/(x…

Evaluate lim (x->0) ((1/x^2)-(1/sin^2 x)) Problem Solution Problem Evaluate lim (x->0) ((1/x^2)-(1/sin^2 x))   Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x -…

Evaluate lim (x->0) (x ^ 2 + 2 cos x - 2 ) / ( x sin^3 x) Problem Solution Problem Evaluate lim (x->0) (x ^ 2 + 2 cos x - 2 ) / ( x sin^3 x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan…

Evaluate lim (x→0) (tanx -x) / (x^2 tanx) Evaluate lim x -> 0 (tan x - x)/(x ^ 2 * tan x) Problem Solution Problem Evaluate lim (x→0) (tanx -x) / (x^2 tanx) Evaluate lim x -> 0 (tan x - x)/(x ^ 2 * tan x) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x…

Evaluate lim (x→0) [1/x - log(1+x)/x^2] Question Solution Question Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type 2 Problems Evaluate lim x -> 0 (tan x…

Evaluate lim (x→0) [a/x - cot x/a] Question Solution Question Evaluate lim (x→0) [a/x - cot (x/a)] Evaluate lim (x→0) ((a/x) - cot (x/a)) Type 1 Problems Evaluate lim (x→0) (x e^x -log(1+x)) / x^2 Evaluate lim (x→π/2) log(sin x) / (π - 2x)^2 Evaluate lim (x→0) (sinh x - x) / ( sin x - x cos x) Evaluate lim (x→π/2) log(x-π/2) / tan x Evaluate lim (x→0) [a/x - cot x/a] Evaluate lim (x→0) [1/x - log(1+x)/x^2] Type…