Let C be the shortest path that connects a to ni and I = fe (sinhz + 1)dz. Then None of these |=-1-cosh Tt+ r(i-1) O I=-1-cosh n+ n(1-i) ΙE-sinh π+ π(1-1) |=-sinh Tt+ T(i-1)

Q: 4. Prove that the equation x + sin(x) = 1 has at least one solution in the interval |3D Va + 3 (0,…

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Q: Do the functions y, = cos4t and y, = sin4t constitute a fundamer %3D The functions constitute a…

A: The given differential equation is y''+4y=0 the auxiliary equation is D2+4=0 D2=-4D=±2i therefore…

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: 2.3 Find the general solution of p fanx+q tany =lanz

A: Given:   P tanx+q tan y=tanz→           1   is of the form pP+qQ=z:

Q: 2.3 Evaluate the integral sinh 2 dz, 7 3i (z – 2i)4 2i 2+ 4 where C is the circle |z – 2i| = 4…

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Q: 9. Use the Secant method to find an approximation to the solution of sin(x) - e-* = 0 in [0, 1]…

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Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: Find the critical numbers of f(0) = 2 cos 0 + sin² 0.

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Q: Find the maximum possible error in the computed value of the hyperbolic sine function, sinhx = at…

A: Solution

Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: Let C be the shortest path that connects a to zi and I = f. (sinhz + 1)dz. Then None of these…

A: Second option is correct answer i. e.  I= -1-cosh(π)+π(i-1) . Thankyou !

Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then Ι-1-cosh π+ π(-1)…

A: For the first question . Option first is correct answer . Thankyou !

Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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Q: iii) E(-1)"+1 cos²(÷) COS n=1

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

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Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: Use the Bisection method to find the solution accurate to within 10-5 for 2x cos (2x)-(x+1)230on…

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Q: 2 3. sin³x cos³x dx OSx Show two solutions. 0.

A: Given  The integration is I=∫0π2sin3x cos3x  dx.

Q: The standard form of 3dy-xydx = 3y3e4x/3  by Bernoulli's equation is:

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Q: Evaluate the integral: f sin 7x cos 2x dx. A) sin 5x + sin 9x + c. 2 B) cos 5x +co cos 9x + c. 10 C)…

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: Find the total length of an astroid x2/3 + y2/3 = 22/3, which can be parameterised as x = 2 cos³ 0,…

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Q: A stretched string of length 20 cm is set oscillating by displacing it midpoint from the rest…

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Q: B- Find the solution to the equation = k satisfying the conditions at ax2 1-- 30 at x 0 for all…

A: A

Q: Show that cos 3x = 3x has a solution in the interval [0, 1]. Hint: Show that f(x) = 3x – cos 3x has…

A: solution:-f(x)=3x-cos3xapplying intermediate value theoremintermediate value theorem states that if…

Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: 4.4. Show that the function f(x) = Sx² cos 1, if x = 0, ૨૦. if x = 0 is a BV-function over the…

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Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

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Q: iax Solue the integral complex path integreil (Residue) 4. dx with the -x2 +2ix +1 method.

A: A

Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: Solve the line integral if path A is a0- (-2+2i) Al= 0+2i A2= 0-2i A3 - 2-2i (3+ 2 )' dz A

A: In mathematics, a line integral is an integral where the function to be integrated is evaluated…

Q: Give two examples of the situation with the solution clearly and in order Soperties of Bessel's…

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Q: capacitor is constructed with two parallel metal plates each with an area of 0.61 m2 and separated…

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Q: Scos cos 3x -1+ cos 5x - dx

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Q: Evaluate the integral. sin (8t + 9) -dt. cos (8t +9) sin (8t + 9) dt%3D cos (8t+ 9)

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Q: Let C be the shortest path that connects 7 to ni and I = f. (coshz + 1)dz. Then --sinh π+ π(1- )…

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Q: Ti Ti to 8 Integrate cosh(4z) dz, C any path from - 8 Use the first method, if it applies, or use…

A: Using:- sinhx = -isin(ix)               Sin(-x)=-sinx               Sin (pi/2)=1

Q: Suppose that the position of one particle at time t is given by X1 = 5 sin(t), Y1 = 2 cos(t), osts…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – -dy y? (1,2) Moreover evaluate…

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Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Find Z in (1-j5) 2= tanh cos lat5 express in lagarithm Form

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

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Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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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.