00 2. It is well known that /e-* dx = VT . Use this fact to prove that / V- In xdx 2 -00

Q: n Rị |1-Ri Lecen (A) = II [A exp(-AZ,)]“ [exp(-ar)] z.)][exp(-Ar)]" i=1

A:

Q: Suppose X~U(0,8).  Find P(x < 5).  Enter the exact numeric value.

A:

Q: Q2] Find the lower bound of Iz - 3|if |z - il < 1

A:

Q: cide whether the following function is one-to-one and whether it is onto. Then prove your answers…

A: In this question, concept of one-one function is applied. One-to-one function The term "one to one…

Q: Let X~Bin(10, 0.3). What is P(X<2)?

A:

Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: = { [" -d] | a,bER} a X = Prove that and X* are isomorphic

A:

Q: Prove that for a # -1, a>0,n EN IS (1+a)^ n >=1+na.

A: Here let A=(1+a)n, a≠-1, a&gt;0, n∈N and B=1+na

Q: Prove or Disprove: The set A = {e^x : x × R} is uncountable, where R is the set of real numbers.

A:

Q: Frod the averuge vearlue of the durndkam f over Shoe lad eraual [q,9]

A: Given function is fx=9x3. Need to find the average of f on -9,9. The average of the function f on…

Q: dx Sx²+ 4 2. 多.区

A:

Q: Find the negation of the quantified expression Vx³y(x² = 2^ y³ = 3) given the domain consists of…

A:

Q: Simplify (m^(wv-m)) to -mv-w 1. Select a law from the right to apply -(m^(wv-m))

A: (  Applied distributive law:    )…

Q: < Use exact numbers. y = ←++ x+ -9-8-7-6-5-4-3-2 9 8 7 23456 6- 5- 4+ 3 2- 1- ST -4 -3- -5- Y -6- -7…

A: from given graph two points on line are (-2,0)  and (4,1)standard form of line is y=mx+cwhere m is…

Q: Find yp for y" + 5y' + 4y = -2x + 3 1- O Option 1 XIN 2 +8+ C

A:

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

A:

Q: Prove that E (2s+l)=3n" whenever 'nisa psitre r'nisa pisitive intger. 32.

A: Given that,      ∑j=n2n-12j+1=3n2, n is a positive integer

Q: P → (Q → R) is equivalent to A. (P ^ Q) → R B. (P v Q) → R  C. (P v Q) → ∼R D. None of these

A:

Q: Let X N(10, 23). Then P( X< 10) = %3D

A:

Q: Simplify (qq) to F 1. Select a law from the right to apply -(q→¬¬q)

A: We have to simplify the logical expression

Q: 5 7x-5+3x VX S³₂0 -2 -) dx

A: ∫-25 7x-5+3x-2x4dx

Q: True or false: Ftaut (p (q=r)) → (p = (q → r)) ? → Select one:

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: n! Verify that Ex1+…+xr=n,xi20 r^n for any r, n>1 x1!x2!...xr!

A: Consider the given information. Let n is greater than equal to 1 arbitrary. Use the mathematical…

Q: 2x-7 x+1 + x - 3 f lelog MATH is an isosceles trapezo and m/H= (x + 3)°, find mzt

A:

Q: Evaluate ∫ ∫σ x^2 + y^2dS, where σ is the portion of z =√3(x2 + y^2) for 0 ≤ z ≤ 3. Exact answer is…

A:

Q: find the power serie representation of( (x-2)^6)/e^x n=0 to infinity

A:

Q: Fill the Following blanks with the right answer! □ PIZ-1.39)= @ P(Z > 1₁96) = Plo. 65 17)

A:

Q: state formally the Heine-Borel Theorem in R^k

A: Let S be a subset of ℝk. Then the Heine-Borel theorem states :

Q: (15 49)} = at* e²¹ sen(71), et 2-¹ {-98 (8-2)² +49)} = What's the value of a*c?

A:

Q: Find yp for y" + 5y' + 4y = -2x + 3 1- Option 1 x 2 +8+C

A:

Q: Find e^z in the for u + iv if z = 11πi/2. (use 3 decimals)

A: Given z=i11π2 We have to find ez in the form u+iv

Q: If x = 3.1 × 10^4 and y = 2.4 × 10^–7, calculate the values of the following, expressing your…

A: Algebraic operations help to find the given expressions. Since the given expressions are the…

Q: (P^Q)^(P = ¬(Q^R))^(S = R) = -S

A:

Q: Let p=17. If a belongs to F_{17} and a is non zero , compute the value of a^{16}(mod 17) for a=3 .

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.