Calculus Answers

Is the function h(u,v)=cos⁡(u)+e^nu+√(sinh⁡(u^2 )+√(v+e^nu ))   , Where n is second digit of your arid number for example if your arid number is 19-arid-12345 then choose n=2. Is is continuous? In case of yes then find the points of continuity. Explain briefly

Define h(0,0) in such a way that h is continuous at origin here n=5

h(u,v)=ln⁡((nu^2-u^2 v^2+nv^2)/(u^2+v^2 ))

Is the function h(u,v)=cos⁡(u)+e^nu+√(sinh⁡(u^2 )+√(v+e^nu )), Where n=5 Is is continuous? In case of yes then find the points of continuity. Explain briefly

Improper Integral (Integrals with Infinite Limits)

∫dx/(x^2-2x-3) from 0 to 4

Improper Integral (Integrals with Infinite Limits)

∫dz/(z-1)^(2/3) from 0 to 2

Improper Integral (Integrals with Infinite Limits)

∫dy/√(y-1) from 5 to ∞

Improper Integral (Integrals with Infinite Limits)

∫e^x dx from - ∞ to 1

Improper Integrals (Integrals with Infinite Limits)

∫dt/t^3 from1 to ∞

Integration by Partial Fractions

1.) ∫dt/(1+sint+cost)

2.) ∫dy/(5+4cosy)

Integration by Partial Fractions

1.) ∫dy/(5 secy+4)

2.) ∫dx/(3-5Sin2x) from 0 to π/4