4:31 PM P P MTH 211 Assignment Attention Answer Sheet: Foolscap Submission Mode: Individual MTH 2...ment Submission Day and Time: Friday, 8:00 AM - 10:00 AM, 2024 Submission Venue: Lecture Theater B (LTB) 1. If V is a homogenous function in x, y of degree a find X +Y av av By -? 2. Maximize (i) f(c,d)-cd subject to (c,d)-c+d-1-0 (i)V-abcsubject to 4(a+b+c)-12a 2xy-1 ab+4 3. Evaluate the following limits lim- lim- limtan"(a/b) [√²+dxdy 5. Given the piecewise function y(x)- evaluate k (= ((x)) 4. Using substitution x-rcose and y-rsine, evaluate (cos² if x 5/2 sin, if x>/2 6. Find the domain and range of the function f(x)=√4-x. 7. Obtain the closed form of fourth order Maclaurin's series evaluation of cos0.25 8. Given that that devaluated. 9. If f(u,v)-av-avevaluate fuf 10. If is a homogenous function of a,b of degree c, and z-f(u)then au¸+bu̟ =? 11. If z is a homogenous function of a,b of degree, and z = f(u) then a'u +2abu+b²=? 12. If f(x)-and g(x)=√x. then the derivative of f(g(x)) is (a)-√xxx²+1)* (b)-(x+1)* (c)-2x/(x²+1)* (d)(x+1)* (e) 2√x(x+1) dy dr 13. If y asinet +bcoset, where a, b and c are constants, then is (a)ac² (sint+cost) (b)-c³y (c)-ay (d)-y (e)a'e sinet-b²² coset) 14. Ir V-sec x+y=? 15. Obtain the stationary points of the function f(a,b)-a²+b²+6+12 16. The Langrangian function F corresponding to a function y,(x)subject to the constraint y,(x)-Ois 17. Evaluate(x+yddy 301 07​