2. The number of hours of daylight in the SMH Lower Forum in month t of the year (with t = 0 being January) is given by the following function. d(t) = 3 sin(t – 2)|] +:

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

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Q: If tg(t)dt = sin(x) for every x, find g(2 1). g(2 x) =

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Q: 1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) nt = 23,…

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Q: 15. Find a) fxedx b) dx using the substitution of x- cos t.

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Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0, f(x) has a root in - f [o]. If we…

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Q: Given t2 – 4 f(x) = dt 1+ cos2(t) At what value of x does the local max of f(x) occur?

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Q: Find an antiderivative of the given function. 4 cos 9x O A. sin 9x O B. - 36sin 9x O C. sin 9x O D.…

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Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

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Q: 1.4 1. Calculate an approximate value of the integral So5 (sinx – Inx + e*) dx by dividing the…

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Q: 1. Calculate for one real root of tan x = 4x with xo = 1.2 up to six decimal places using the…

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Q: For each of the following problems differentiate the given function. 1. T(=)=2 cos()-6cos ()

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Q: Find a possible formula of the form A sin t + k or A cos t + k for the periodic function with a…

A: Given formula is: A sin t + k or A cos t + k

Q: 1. Calculate for one real root of tan r 4x with ro 1.2 up to four decimal places using the…

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Q: 2. Find L{f(t)} if f (t) = = cos 4t + t-1/2 + e5t – sin 3t – 5t – 1.

A: We will use the formulas Lcos at = ss2+a2Leat = 1s-aL(sinat) = as2+a2L(tn) = n!sn+1 Hence we have…

Q: Find a first-order L²-approximation for the following equations f(x) = sin x f(x) = e-3x 0≤x≤1…

A: We have to solve given Questions.

Q: Given x2 + 11x + 18 f(t) 1+ cos (x) At what value of t does the local max of f(t) occur? t =

A: Solved below

Q: Obtain the general solution of the following: 2. -z (2- 2) sec'e 3. xdx + sin () Lydx - xdy]

A: 2. The given equation is  dθdz=z(z-z2)sec2θ This can be written as…

Q: The number of hours of daylight in the SMH Lower Forum in month t of the year (with t = 0 being…

A: Note:- As per our guidelines, we can answer the first three sub-parts of the problem. Please…

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: Find approximate solution of the following Abel's problem: sinx = u(t)dt.

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Q: Prove the following: d -1 arccos(x) dx V1- x2

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Q: For each of the following problems differentiate the given function. 1. T(=)= 2cos(:)+6cos (=) 2.…

A: We are to differentiate the given functions1. T (z) = 2 cos (z) + 6 cos-1(z)2. g(t) = cos-1(t)-4…

Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

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Q: Find the greatest value of F (x)= | (6 . cos t - 2 sin t) dt 5 7/3 in the interval [5/3,7 t/ 4|.

A: Fro the given problem: Fx=∫5π/3x6cost-2sintdt Now solve the above definite integral,…

Q: Find the solution of the following problem accurate to within 10-5 using the Secant method. In(x -…

A: Secant method is one among different methods used to approximate the zero of a function within an…

Q: Differentiate the following functions: e2x+1x +2 .3 a) f (x) = sin (3x+2) %3D -1 sin(3x) V3t? +t-3…

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Q: Show that where n is a positive integer.

A: To show

Q: :- x2 + 10x + 24 dx. 1+ cos2 (x) f(t) = %3D At what value of t does the local max of f(t) occur? t =

A: Given: ft=∫0tx2+10x+241+cos2xdx

Q: 1 1. The function Y = sin(t² )+ 4 is graphed below. Define F(x) = [, sin(1²) + - 1 dt 4

A: Given: F(x)=∫0xsint2+14dtThus, Fx represents the area under the curve y=sint2+14(a) First of all we…

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: The linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is:

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Q: Find the solution of the following problem accurate to within 10 using the Secant method. In(x – 1)…

A: Given function is ln(x-1)+cos(x-1)=0 and 1.3≤x≤2 So f(x)=ln(x-1)+cos(x-1) Let x0=1.3, x1=2 So…

Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: - Suppose that for a certain leat-cutter ant colony, the birth rate is modelled by: B(t) = 23,000 –…

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Q: 22: Find dyldx for the following functions * (40 marks) · y = In (3 – 4 cos x) + (4x – 5)5 2. y = x²…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) +…

A: Answer

Q: IV. Suppose z is a function of r and y, and tan y2 + x² = 2*e. Solve for az dz and %3D dy

A: To solve for dz/dy and dz/dx.

Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: 1 In order to evaluate dx, the correct substitution is V-x²–4x+21 None of these -2 + 5 sin(t) x = -2…

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Q: 1. Suppose that the rate of gasoline consumption in the United States (in billions of gallons per…

A: We shall answer first three subparts as per the guidelines. You can post it again by mentioning…

Q: Find the smallest value of t such that t>0 and sin(8t)– sin(3t) =0.

A: The given equation is sin8t - sin3t  = 0 or,  sin8t  = sin3t or,  sin8t  = sin(pi-3t) On comparing…

Q: Given that f(x) = V3 cos 5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a…

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Q: Suppose that ay" + axy' + by = 0 has the general solution of the following form: y = x=1(C1 cos (3…

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Q: 1. Suppose that for a certain leaf-cutter ant colony, the birth rate is modelled by: B(t) = 23,000 –…

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Q: 24 Show that the solution of equation satisfying the condition O T-0, as t0 (1) T-0, for x-0 and x=a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

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Q: Q1\ Prove the left side equal to right side in the following : * L-1 (s² + a²y² - [sin at + at cos…

A: We need to show that:L-1s2s2+a22=12asinat+at cos atWe will use convolution theorem to show the…

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.