· Problems • Show that • 1. ~(p ^q) = ^p ^ ~q

Q: 1. f(x)= sqrt(x^2-4) Where is the function positive? A) [0, infinity) B) (2,infinity) C) (0,…

A: 1) Given: sqrt(x2 - 4) we know that square root is not defined for negative input as we will get the…

Q: · Problems • Show that 1. (p ^q) = vp A~q 2. ~(p → q) = p ^ ~q

A: We have to Solve given equivalency by Truth Table Method.

Q: Let S = Span}( 3 2 3 . Show that dim(S)=2. 3

A: Basis: Let V be a subspace of ℝn. A basis of V is a set of vectors v1, v2, ..., vm in V such that:…

Q: 1 хах 'o V1-x4 V3 xdx

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Q: Let F(x) = f(x7) and G(x) = (ƒ(x))¹ . You also know that a = 7, ƒ(a) = 2, ƒ'(a) = 15, ƒ'(a¹) Then…

A:

Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: he professor collects data from 65 randomly chosen students. The estimated OLS regression is: Y = 45…

A: B option is correct as we want to check that, there is any significant effect of x on y or not. So…

Q: 8.) FIND ALL DERIVATIVES OF y^(n) OF THE FUNCTION y = square root of (x+5).

A:

Q: What are the critical points and inflection points of the equation 1/(x(x+1)^2)

A: In the question it is asked to calculate the critical points and inflection points of the equation.…

Q: Evaluate xy’ + 2y = x^4 a. 6x*(y^2) = x^6 + C b. 6y*(x^2) = x^6 + C c. 6xy = x^6 + C d. 6y = x^6 + C…

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Q: . How we Can Solne it ? 2. *B" (K+t) Carzz) (a+3) KB (ati) (a+2) %3D

A: Some formulae's: (a+b)2=a2+b2+2ab Power addition: (xayb)(xcyd)=xa+cyb+d

Q: Suppose / (x)= - . What is the value of f "(-2)? A B D

A:

Q: will x-x1²= f(x) = 2x²10 X X²+3x-10

A: Solution is given below:

Q: 10) [2* dx

A: given,         ∫2-4xdx

Q: (? + 5 )2y = 3r(y² + 1)- -(a+ + 8x² + 9)y, y(1) = 0 4+8 (,? + 5),'

A: solve the given equation by separable method:

Q: Question 1. Identify the correct description for the formula Su (s) \approx \dfrac{u(s+h)- 2 u(s) +…

A: Step:-1 Note:- Central finite difference formula for second derivative is f''x≈fx+h-2fx+fx-hh2 with…

Q: (3) 1 9 x (1 + 4log²x) dx a) ≤ arcta Carctan (210 +2 Laretanly log) 45 36 Starctan (2 log) 47…

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Q: 2-fx'e-2x* dx

A: To evaluate: I=∫x3e-2x4dx Substituting x4=u⇒4x3dx=du⇒x3dx=du4

Q: The volume V of a right circular cylinder of radius r and height h is V = ar?h. (a) How is 4 related…

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Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: +ay'- - 3X = 0

A:

Q: 7. Find : y = (x* = 5«)a0n 5x, (b). y = x2

A: We can find the derivative as below

Q: 49' class is shown in Figure 1. RUN mpetitors in the '40 to CYCLE SKI Run, cycle and ski times for…

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Q: 6.72 Evaluate (a) and (c) Give the EXCEL function for parts (a), (b), and (c).

A: Every set of data has different type of arrangements. It is possible to study the arrangement of…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.