Question

Simplify the following Boolean functions, using K-maps. Find all the prime implicants, and determine which are essential:

(a) F (w, x, y, z) = ? (1, 4, 5, 6, 12, 14, 15)

(b) F (A, B, C, D) = ? (2, 3, 6, 7, 12, 13, 14)

(c) F (w, x, y, z) = ? (1, 3, 4, 5, 6, 7, 9, 11, 13, 15)

Answer #1

Using K-map to simplify the following Boolean function:
F(A,B,C,D) = m(1,3,5,6,7,9,11,12,13,15)

Using K-map to simplify the following Boolean function:
F(A,B,C,D) = å
m(1,3,5,6,7,9,11,12,13,15)

Find the derivative of each of the following functions:
(a) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(b) y =63 (d) w=3u^(-1) (f) w=4u^(1/4)
2. Find the following:
(a) d/dx(-x^(-4)) (c) d/dw 5w^4 (e) d/du au^b
(b) d/dx 9x^(1/3) (d) d/dx cx^2 (f) d/du-au^(-b)
3. Find f? (1) and f? (2) from the following functions: Find the
derivative of each of the following functions:
(c) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(d) y =63 (d)w=3u^(-1) (f) w=4u^(1/4)
4.
(a) y=f(x)=18x (c) f(x)=-5x^(-2)...

For the given functions, find y′ . You do not need to simplify
the answer.
a. f(x)=(3x^2)ln(5x+4)
b. y = e^(4x-3)/(2x^2-7)^2
(2x2 −7)

Find the truth table (function table), SOM, POM, and
simplify the expression using K Map approach of the following Sigma
notation expression: (10 points) f(w,x d y,z)= sum
m(0,3,9,10,14,15)

Find the derivatives of each of the following functions. DO NOT
simplify your answers.
(a) f(x) = 103x (3x5+ x − 1)4
(b) g(x) = ln(x3 + x) /
x2 − 4
(c) h(x) = tan-1(xex)
(d) k(x) = sin(x)cos(x)

Write a C++ program to demonstrate thread synchronization. Your
main function should first create a file called synch.txt. Then it
will create two separate threads, Thread-A and Thread-B. Both
threads will open synch.txt and write to it. Thread-A will write
the numbers 1 - 26 twenty times in nested for loops then exit. In
other words, print 1 - 26 over and over again on separate lines for
at least 20 times. Thread-B will write the letters A - Z...

In the following functions: a) Find the gradient of f. , b)
Evaluate
the gradient at point P. and
c) Find the rate of change of f in P, in the direction of
vector.
1- f(x. y) = 5xy^2 - 4x^3y, P( I , 2), u = ( 5/13, 12/13 )
2- f(x, y, z) = xe^2yz , P(3, 0, 2), u = (2/3, -2/3, 1/3)

1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
(e) j(x) = ln(x) / x5
(f) k(x) = ln(cot(x))
(g) L(x) = 4 csc^-1 (x2)
(h) m(x) = sin(x) / cosh(x)
(i) n(x) = 2 tanh^-1 (x4 + 1)

Evaluate the following:
1) ∫ 4? ?? and determine C if the antiderivative F(x) satisfies
F(2) = 12.
2) ∫4???=
3) ∫( ?5 + 7 ?2 + 3 ) ?? =
4) ∫ ?4( ?5 + 3 )6 ?? =
5)∫4?3 ??=?4+ 3
6) ∫ ?2 sec2(?3) ?tan(?3)??
7 ) ∫ 53 ? 13 ? ? =
8) ∫ ln8(?) ?? =?
9) ∫ 3 ln(?3) ?? =?
10) ∫ 4?3 sin3(?4) cos(?4) ?? =
11) ∫6?55?6??=
12) ∫???2(3?)??=
13)...

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