Proofs. (A) 1. ADD 2. (A• D)>F IADF (B) 1. (A v B) > (C • E) 2. (D E) F IA F (C) 1. M (Q v R) 2. (M> R)> (P• S) 3. QR IS

Q: P= (2,3,4) Q =(4,6,8) Check my work: rlt) = [(4,6,8)-(2,3,4)].t 6667-₤14,6,8) (2,304) r(t) = r' (t):…

A: The given function is f(x,y,z)=z2, and the points are P(2,3,4), and Q(4,6,8). We need to check…

Q: -3z + 4, a < -2 22 - 2, 2-2 18. If f(x) = find f (-2). || A. 10 В. 2 C. -2 D. -6

A: Given function is fx=-3x+4, x&lt;-2x2-2    ,x≥-2.

Q: Determine |-5 (cot2 (4x + 7) + 1) dx.

A: Given∫-5cot2(4x+7)+1dxUsing identity :1+cot2x=csc2x=∫-5csc2(4x+7)dx

Q: 3. (D² +1)y=tan (x)

A:

Q: a² f If f(x, у)— 3х'у +9х, then дхду a. 6x? b. 9x? c. 9x²y С. d. бx? +9

A: Evaluate the given differential of the function f(x, y) = 3x3y +9x   Find the d2 f/dxdy

Q: (x-2)² + (y+1)² =16, find- A. 16 (y+1)³ d²y dx² B. 16 (y +1)³ C. 16 y³ D. 16(x-2)² (y+1)³

A:

Q: Find the interval(s) where f(x) = 2x° – 15x? + 36x – 27 is increasing. -

A: The given function is fx=2x3-15x2+36x-27. The main objective is to find the intervals where the…

Q: 1 1-¹ ( ( 5 + + 2) ³) 3 = Find ac + b. α ~tbeat C

A:

Q: c. x = t3 and y = 2t2 /2, 0<ts v3 3 d. x = t2/2 and y = (2t + 1)7/3, 0<t< 4 %3D

A: 1)x = t3  &amp; y = 2t22,  0≤t ≤ 32)x = t22  &amp; y = (2t + 1)323,  0≤t ≤ 4

Q: 5. Evaluate f V2x + 1 dx. (2x + 1)/2 + C a. 3. b. (2x + 1)/2+ C c. (2x + 1)/2 + C d. (2x + 1)/2 + C

A:

Q: q.1.x, q.x² q.1.X + d²w_S.w dx2 D 2. D 2. D Solve the ODE ( S>0, D>0, q > 0, 1> 0)

A:

Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)?) = 2a3 Find the value of a . إضافة…

A:

Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²)= 2a3 Find the value of a .

A:

Q: An object moves along a straight line and it's velocity (v) in ms¹ at time (t) in seconds, is given…

A: Sol:- v = 5-4t3Velocity can be written as 4t3dsdt=5-4t3ds=5-4t3dt

Q: 1 4. (1+2)y/ + 2ry = (1+2)y

A:

Q: /2-x2 Evaluate *Ty dy dx x²+y² Select one: a. Non of them b. 1 2 - V2 С. 1 1 V2 d. 1 3

A: We will find out the required value of given integral.

Q: x²-x 2)) S dx =? |x-1|

A:

Q: 6x² + 7x – 6 dx (x² – 4)(x +2) 38. Evaluate

A:

Q: Ex: If f(3) = 0, show that əz дz x- x² + y = Z. (H.W.) əx Əy

A: We have to prove the given statement.

Q: x* - x x2 + x+ 1 et dx 1+e*

A:

Q: df find dz

A:

Q: for power substitution method, next step is * For f V1+ Vx dx - (u*) (2udu) - [u? (2udu) Option 1…

A: We have to find the correct option from the given options.

Q: The velocity, in feet per second, of a rocket t sec into vertical flight is given by v(t) = –3t² +…

A: To find an expression h(t) that gives the rockets altitude in feet,t seconds after liftoff.

Q: Find and a and дхду f(x,y) = x2 - y2 + 6xy + 4x – 8y + 2 a. b. f(x, y) = e*y + xy

A:

Q: The solution of the ODE: y' +y = x² +2 y=j ex*/5 (x² + 2)dx + C None is:- y.e/5-fe*/5 (x² + 2)dx +C…

A: Topic = Differential equation

Q: Find (3x + 5y)dA where D = {(x, y) | {(x, y) | x² + y² ≤ 4, x>0}

A:

Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: Using simplex method whot is the entering variat

A: Given,          Max.(Z)=12x1+16x2 Subject to            10x1+20x2≤120                8x1+8x2≤80…