If y=sin(x), z-cos(x), v=sawtooth(x), e=rand(4), where 0

Q: If sin y =x sin (a +y) then show that dy sin (a +y) (a is not multiple c dx sin a

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Q: Find the quadrant in which the terminal point detemined by t lies. sin(t)<0 and cos(t)<0…

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Q: H.w Find the enlsed between yasinx, ya cas X arca

A: In the question it is asked to calculate the are enclosed between y = sin(x) and y = cos(x) when x…

Q: If y = cos? x – sin? x, what is y? X - х, | dx

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Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: dy sin(x) Find for y = dr -3

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Q: :? If sin(x +y) = xy, what is the correct expression for dx cos(x+y) - y x- cos(x+ y) A cos(x + y) -…

A: for this problem, we can solve this by using general implicit  differntiation.

Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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Q: Let y = (sin z+ cos r)e", x E [0, 27]. %3D

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: d" y If y= cos x, then d x5 (A) -sin x (B) sin x (C) -cos x (D) cos x

A: This is a problem related to differentiation of the function. Based on the general formula and…

Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: f(1, y) = cos cos y is = COS I COS y

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Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

A: Given : r(t)=3cos(t), t-4, 3sin(t) is the position function of a particle. To find : If the particle…

Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: The value C in y = sin (Bx +C) is called the _________.

A: The given equation is y=sinBx+C

Q: (y – x)dx + (2x – y)dy or the given path. C: x = 2 cos(8), y = sin(8), o se s 27

A: This is a problem of vector calculus.

Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

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Q: Of the following, which are acceptable wavefunctions in the range x = -infinity to infinity and…

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Q: Eliminate parameters A and B but not parameter C by differentiating x with respect to t. x=A sin…

A: The given equation is: x=Asin(Ct+B)

Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: Eliminate the parameter t from the following. Sa(t) = 2 sin t + 5 ly(t) = 5 cost – 6

A: Rewriting the given equations:

Q: Choose the only equation below that does NOT represent a circle. Ox =1+ 4cos(t) y = 3+4cos(t) O x2…

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Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

Q: If x = sin2 (u) and y = cos² (u), then dy is : dx а. 1 b. cot(x) C. tan(x) d. 1-

A: Differenriate

Q: If f(u) = e¯sin y + 7 cos y, find f'(y). Use exact values. %3D f'(y) =

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Q: SITUATION 5. Find du/dx for the following: * (€);y = VT+ 1 +x² 37. u = sin-1

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Q: ad boda noY BAJUM 7. Find dy/de. dimil nom y = sin [cos(tan 0)]

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Q: If y = (tane) /28 +1 find dy then choose the correct answer: %3D dx

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Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: If y = (sin¬1 x)², show that dy (1 – x²) da? dy = 2. dr

A: y=(sin-1x)2 we have to show  (1-x2)d2ydx2-xdydx=2

Q: Find and y" for y = 0 cos e. %3D

A: y=θcosθdiff w.r.t θdydθ=-θsinθ+cosθdydθ=cosθ-θsinθ y'=cosθ-θsinθ

Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

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Q: The cos'ydy is equal to 3 1 A. siny + sin³y + sin³y -; sin'y + C 5 3 B. siny – sin³y +sinsy -sin?y +…

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Q: Find the value of dw / ds at s = 0 if w = sin (e√r) and r = 3sin (s + π/6).

A: w=siner,  r=3sins+π6 Differentiating w=siner with respect to r, we get…

Q: e* cos e* dx J 4 + sin²e* A 1 tan-1 2 sin e* + C sin? e* + C 2 2 tan-1 B sin e* tan- 2 1 tan-1 2…

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Q: At what point does the sine function y = sin x, cross the y axis? O (T, O) O (0,0) O (1,0) O (0,1)

A: Given  function is y=sinx. We have to find the point at which the function y=sinx cross the y-axis.…

Q: If the position of a moving object is s(t)=(sin t)² meters above zero at t

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Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

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Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: Set C: Problem #6 Fina the equgtion of the line tangent tO FCx)= cas?x - sin² () at x = 2JL

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Q: If f(x, y) = e“ sin(4y) then: 4 sin (4) 4 cos( 4) V f( – 1, 1) . el el

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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.