(2) Let (x)S Hg(x)S Hc(x). Prove that AN(BỤC)=(ANB)U(ANC).

Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: We have to find out the operation

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: true false f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both antiderivatives of cos(x).

A: f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both anti derivatives of cos(x).

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

A:

Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: 6. Let a be a positive constant. Determine the general antiderivative of a using the fact 1 a² + x2…

A:

Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

A:

Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

A:

Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

A:

Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

A:

Q: Verify Young's Theorem y? x2 z = In(2x + y) – + e(x+2y) + - y

A:

Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: 4х+2 Evaluate the integral -dx. (Hint: Use Algebra to help further rewrite your (x² +1)(x=1)…

A: First break by using partial fraction then integrate

Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: Given: xD(D+x)

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

A:

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

A:

Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 1 Evaluate the improper intergal | dx (x2 + 9)° using the residue theorem.

A:

Q: 2 Evaluate the improper integral e2a dx, if exists.

A: Evaluate the improper integral  ∫-∞2 e2x dx

Q: the Fundamental Theorem of Ca -5 (x³ – 9x)dx. v3

A: Here we have to use fundamental theorem of calculus to find the exact value of  ∫05(x3-9x)dx…

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

A:

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

A:

Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

A:

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: 4. Compute dx S in two ways and verify that the answers agree.

A:

Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: 14. Give the linear near-minimax approximation for f (x) = sin a on [–1, 1].

A: To determine linear near-minimax approximation for fx=sinx on -1,1 Let the approximation be px=a+bx…

Q: Find the most general antiderivative of: f(x) = 4√x − sec(x) tan(x) + (7/(x2+1))

A:

Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: Define (a) P.T. f(x) 0. (b) P.T. f(x) = x+1 [*** sin(1²) dt x 2x f(x) = cos(x²) - cos[(x + 1)²]…

A: Note: As company policy, we solve first three sub-parts only. Please resubmit the remaining…

Q: Find the most general antiderivative of: f(x) = 4√x − sec(x) tan(x) + (7/x2 +1)

A:

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

A:

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

A: To find out the volume of solid of revolution.

Q: In(x) -dx Evaluate the integral m(2)

A:

Q: 2 Evaluate the improper integral 4x e dx, if exists. 8.

A: Given that,           ⇒           ∫-∞2e4x dx   ,   if exist             ⇒         find the…

Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

A:

Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

A:

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: 1 Evaluate the improper intergal dx (x² + 16)² using the residue theorem. 8.

A:

Q: RA Find dx dt x In(x) /1 + (In(x))²

A:

Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

A:

Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

A:

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: Use the second fundamental theorem of calculus along with the chain rule to find d sint dt dx 1 o…

A:

Q: Show that * Ső› X yn+¹ J₁ (xy) dy=Jn+1 (x)

A: Using the recurrence relation of bessel function

Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.