The amplitude of a given function f (0) minimum value of f (0) is 3, what is the maximum value? = a cos (k (0 –- d)) +c is 7. If the a) 7 O b) 10 O c) 17 d) 14.

Q: The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cos 0 e = 3rk…

A: Take denominator of f is equal to zero.

Q: - Determine the largest interval in which the unique solution of (t – 3)y +tan t y =t, y(n) =0 is…

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Q: The function yow) satisfies the differantial equation x dy + ay Cos(xx) ak y(1) = 1 , the valu of…

A: Given differential equation is  xdydx+2y=cos(πx)x,y(1)=1

Q: If f(x,y,z)=sin(xy)+x2lny, then fxy at (0,pi/2) is equal to 1 FO

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Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: The orthogonal trajectories of r = 5a sin 0 is, where a is an arbitrary constant r = csin 0 O r5 = c…

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Q: sin t. 15. C/G f()= 2 sint. cost, 12 x.

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Q: Show that the p.d.f. of Z? is given by g1(x) = cosh(vAr), x > 0, wh cosh(z) = }(e² + e-=) is known…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: , Use the Maximum/Minimum Principles to deduce that the solution u of the problem D.E. u = kuzz 0 0.…

A: The differential equation will be, ut=kuxx  0≤x≤π , t≥0 The boundary conditions are, u0,t=0uπ,t=0…

Q: u" (x) = -u(x), 0 < x < T, и(0) — и(т) — 0.

A: Step:-1 Given differential equation of second order is  u''(x)=-u(x), ----(1), with u0=uπ=0 and…

Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: Find the absolute maximum and absolute minimum values of f on the given interval.…

A: Consider the following function f(t)=2cost+sin(2t)Differentiate wrt "t"f't=2sint+cos2t⋅…

Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: Verify that the function u, defined by u(t, x) = t sin(x – t²), is a solution to the equation ,2 U +…

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Q: Let u > 0 be harmonic in R². Show that u is a constant.

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Q: 5. Given a piecewise function sin t, 0st< f(t) = {0, (t, i. Express f(t) in the form of unit step…

A: Given: (i) To express f(t) in form of unit step function (ii) To find L{f(t)}

Q: 6- What is the arclength of the function y = 7x + 2 on the interval [2,6]? a) O /2 90406 b) O 20 c)…

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: 1 Find the local linear approximation of f(x) = , at 3+ 1 Tg = 2, where Az = I- 2. NOTE: Enter the…

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Q: ind c, and c2 so that y(x) = c, sin x+ c2 cos x will satisfy the given conditions. Determine whether…

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Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

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Q: Let / = x tan(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

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Q: A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move…

A: Given force f(x)=x2-cos(3x)+2

Q: -8. AB is tangent to to OC at point B. E 6. MZCDA - 8. MZDBA = 32

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Q: Find the absolute minimum and absolute maximum values of f on the given interval. ft) = 4 cos(t) + 2…

A: This question is related to trignometry, we will solve it using differentiation.

Q: Given f(m) = | | 1+ cos°(?) t2-49 dt At what value of x does the local max of f(x) occur?

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Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: Find the function r that satisfies the given condition. r'(t) = (5, sin 8t, sec ct); r(0) = (3,3,3)…

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Q: The orthogonal trajectories of r = 5a sin 0 is , where a is an arbitrary constant p = c cos 0 r=…

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Q: -a cos y + ze-1/(1+y²), then If f(x, y, z) = el- of ?x ; |(1,0,п) = fæ (1, 0, 7).] (Show solution.)…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval.

A: We find f'(t) using chain rule

Q: Find the maximum and minimum values of the function g(0) = 60 – 9 sin(0) on the interval T 0, 2

A: Introduction: - The peaks and valleys during a function's curve are called maxima and minima. A…

Q: Given f(x) = , 1+ cos²(t) t? - 9 dt %3D 0. At what value of x does the local max of f(x) occur?

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Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: 4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y"…

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Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *(;) + -1 1. 2tan () + -1 2tan…

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Q: Consider the function f defined on [0, 1] such that / (0) = f(1) = 1.f(1/5) = {(3/5) - 2, and /(2/5)…

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Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

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Q: Determine the interval in which solutions are sure to exist. y" + ty" + ty' + t'y = ln(t) Valid on…

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Q: Pracbte 111 co° exist, which statement is most likely true? If the function f(x) has a local minimum…

A: Given query is to find the correct statement.

Q: ). In Chemistry, the Lennard-Jones potential, 12 R V (r) = - 2 r> 0, is a simple function used to…

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Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…