-6 4. Compute x5 + 3x4 + 2x3 + 1 dx.
a box with a square base .6 4. Compute x + 3x4 + 2x3 + 1 -da. 24 일 5. Let F(x) = tet-2+tº +1 dt, find F'(2). tt +3 0 -. A box with a square base and open top must have a volume of 500 cm. Find the dimensions of the box which minimize the amount of material to be used. 2. Draw the graph of f(x) = x ln(1x) - (x - 4) In(x - 41).
#2 #3 #4 please snf thank you :) Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc Evaluate the following anti derivatives (Indefinite integral) 1)「(2x3-5x + 7)dr 3 x ax Evaluate the following definite integrals: 01 2Sec2xdc
3. a) Let f(x) = 2x3 – 4.. Use only the definition of derivative to compute f'(1). b) Using only the definition of right derivative, show that if f(x) = x1/4 then f4 (0) does not exist.
1. Consider the problem minimize f (x1, x2) = x} + 2x3 – 21 – 4x2 + 2. (a) (4 points) Find all of the points (21, x2)T that satisfy the first-order necessary condition (FONC). (b) (4 points) For each of the points in the above question, identify whether it a local minimizer, local maximizer, or saddle point. (c) (2 points) Is there a global minimizer?
please help me with these, thank you. Exercise 34: (The integral of a Gaussian/Bell curve) Let et(1+x2) dr 12 f(t) dr g(t) and and h(t) f(t)2 + g(t) Problem sheet 9 Homework 29. Mai 2019 a) Compute h(0) b) Compute h'(t) for all t 0 Remark: You have to argue why you can interchange differentiation and integration c) Compute lim h(t) d) Use a)- c to show that edr 1 da and _ Exercise 34: (The integral of a Gaussian/Bell...
et What is 1. dr? 1 + 21
Please show all steps. (1 point) Solve the system 13 +2x4 +2x3 1 -21 24 -4x3 94 +163 12x4 +бх4 За1 —Зх2 41 +4x3 X2 2 III| ह
R R 5. To compute 1 = lim 2 COS dr and J = lim 22+1 sinc dx simultaneously .22 +1 R R0 R R using Residue Theorem, let f(x) 22 +1 C COSC sinc (1) Show that if z = x + iy, then Rf(R2) = and Sf(R2) = x2 +1 x2 +1 (2) Find Res[f, i]. (3) Show that I = 0 and J (4) Prove I = 0) in the above problem without using Residue Theorem. IT
6. Compute the orders of the permutations (2 1 4 6 3), (1 2)(3 4 5) and (1 2)(34). 7. Compute the orders of the following products of non-disjoint cycles: (1 2 3)(2 3 4);(1 2 3)(3 2 4);(1 2 3)(3 4 5). Show your work Ans 6. The orders are 5, 6 and 2 respectively. 7. The orders are 2, 3 and 5.