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Prove by algebraic method 1. (a) (10pts) Prove by algebraic method that a+ ab + ač...
1. (a) Prove by algebraic method that ¯a + ab + ac¯+ a ¯bc¯ = ¯a + ¯b + ¯c. (b) Find the CPOS of f(x, y, z) = (x + ¯y)y + ¯xz + x + y + ¯y(x + z).
Prove by algebraic method that a ̄ + ab + ac ̄ + a ̄bc ̄ = a ̄ + ̄b + c ̄.
5. Prove each of the following set equalities both by Venn Diagram and by algebraic method. (a) A - (B C) = (A - B) (A - C) (b) A - (B C) = (A - B) (A - C) (c) A (B - C) = (A B) - C = (A B) - (A C) Hint: To prove the last form, use the equality A C' = A (A' C'). (d) A (B - C) = (A B) (A...
The boom AB is held in equilibriuum by a ball-andsocket joint at A and a pulley and cord system as shown. Determine the x, y, z components of reaction at A and the tension in cable DEC if F=-1500k lb. (Note that pulley at E is at the coordinates x = 0, y = 8 ft and z = 1 ft.) 2. The boom AB is held in equilibriuum by a ball-and socket joint at A and a pulley and...
2.7 Exercises 43 4. Prove each of the following identities by using the algebraic rules (no truth tables). Several steps may be combined, but make sure that each step is clear (a) a'b b'c + a'c (b) а'd + ac (c) xz' + x'y' + x'z + y'z = y' + x'z + xz' (d) ad' a'b' + c'd + a'c' + b'd = ad' + (bc' (e) xy' z(x' + y + w) (f) a'z' yz + xy' =...
02. (2). If |2-3|=|z+il. (1). Use an algebraic method to find a Cartesian equation of the locus of 2 (11) Sketch the locus of zon an Argand diagram. (6). If are 9- (1). Sketch the locus of P(x,y) which is represented by z on an Argand diagram (i). Find the Cartesian equation of this locus. (c). Given that the complex number z=x+iy where x,y e Rssatisfies the equation 12-12-51 = 3, find the minimum value and the maximum value of...
Q7 Prove the real valued function in x and y given by 1) and (ii) are harmonic. Find the corresponding harmonic conjugate function and hence construct the analytic function f(z) = u(x,y) +j v (x,y) 0v(x, y) = In(y2 + x2) + x + y, z = 0 (ii) u(x,y) = y2 – x2 + 16xy
U Prove the following statement using the definition of limits and illustrate with a diagram. (10pts) lim (3x + 1)-2 1 (4pts) Part 1: Find 8 (3ptsi Part 2 ВАМ НЕКА Зpt)
An algebraic closure of a field F is a field K such that: 1) K/F is an algebraic field extension, and 2) every nonconstant polynomial in K[x] has a root in K. If K is an algebraic closure of F, prove that every polynomial p(x) ∈ F[x] splits in K[x].
please explain each of the steps and prove why was it correct for each of the problem and don't use L'Hopital's rule for 2 and 3, thank you. The graph below is the function f(x) 4 3 2 1 -1 3 - 4 -5 d Find lim 12 f(2) Find lim 12+ f(x) Find lim f(x) 12 Find f(2) 2? + 10+ 21 Evaluate the limit using an algebraic method: lim 2-3 2 +3 Evaluate the limit 81 - 2...