Find fry (1,2) for f (x, y) = y?ln(7 + x) +. 23 41 -- 4 23 41 4 27°C Rain showers

Q: dy Suppose =ky, where k is constant and y=8 when t=0. Also suppose that y=6 when t=3. What is the…

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Q: Thank you

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Q: dg 1 дд If g(x, y) = xy + y ln(ry), show that ду + y dr = x+ In(xy). dxðy

A: given: gx,y=xy+yln(xy) we have to show that: ∂g∂y-∂2g∂x∂y-y∂2g∂y2+1y∂g∂x=x+ln(xy)

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

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Q: The velocity in m>s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 +…

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Q: Show that g(t) = t / ( t+1 ) takes on the value 0.499 for some tin [0, l].

A: To show that g(t)=tt+1takes on the value 0.499 for some t in [0, 1]. We use intermediate value…

Q: dy when t = 7. dx Evaluate y = 2z? – 3z + 5 x = 4t +t t = z? +z+1

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: a- If w = x² + 2xy and x, y change from initial values (x = 1, y = 3) By amounts dx = 0.01 and dy =…

A: Given: w=x2+2xy So, dw=2x dx+2y dx+x dy...(1)

Q: Kim throws a ball against a wall at time t = 0 At time t = 1 , it hits the wall and then at time t =…

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Q: Find fæxyzz for f(x, y, z) = z³y² ln(x). [Show your solution.] Select one: O O O x² 6z²y x² 2z³y x²…

A: See this solution in below.

Q: 12. Use the substitution x = sec 0, where 0 < 0 < T/2 or T < 0 < 3#/2, to evaluate Vx2 1 dx x*

A: We will evaluate the given integral by using substitution method as shown below

Q: A particle moves along the x-axis with it's position at time t given by x(t)=(t-a)(t-b) where a and…

A: Given A particle moves along the x-axis with it's position at time t is   x(t)=(t-a)(t-b)  where a…

Q: dy Suppose =ky, where k is constant and y= 10 when t=0, Also suppose that y=15 when t=2. what is the…

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Q: 12. The position of an object at time tis given by x = V3t – 4 ++4, where x is in feet and t is in…

A: (12) The position of an objects at time t is given by  xt=3t-4+1x+4, x is in feet and t is in…

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 - 6t 24.…

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Q: At any time t, the velocity of a particle moving along the y-axis is given by v(t)= 4t - t^2. The…

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Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: 8. (/E= + y² - y) dt + (y/E² – y? - t) dy = 0; when t = 3, y = 4 %3D

A: Solution is  ty=3(t2+y2)3/2 -363

Q: Find the most general antiderivative. 3 4.9 #18 g(v) = 2 cos v V1-v2

A: We will solve the following.

Q: dF Q. IF the value of (t) change from x to x. Find the r(x.t) = (t-x) cos( F(x) = S(x,t) dt for…

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Q: Evaluate /f/2e(*+у*+ dV over B where B - {(a, у, 2) : а? + у? +2? < 1}. Тake п %3 3. SSS 2e(z²+y° О…

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Q: dy Solve the initial-value problem for y as a function of x. (49 – x²). dx = 1, y(0) = 4 Y =

A: We will solve this integration using trigonometric substitution as follows

Q: [B] If Z = 4 cos w – bw, find the relative percentage error in Z at w = 0, if the error in w =…

A: Given that  function is     Z=4cosw-6w we have to find the relative percentage error in Z at w=0.…

Q: d?y taby = Fo cos ot, where wo, ware positive con- dt- stants, and Fo is an arbitrary constant. You…

A: Given differential equation, d2ydt2+ω02y=F0cosωt      ...(1)

Q: Use differentials to find the approximate value of y: (2x – 1)* when x = 0.98. O (E) None of the…

A: Given :f(x)=2x-14x=0.98

Q: dy a. Find of the following. dx x² (x+1) 1. y = In (x+2)3 2. y = (22x e4*)² 3. y = cosh(ln x2)

A: We will use the product rule, quotient rule and the chain rule of differentiation.

Q: Q2: Find the for the following functions: dy dx 1. y = 1- and t = 1/ 2. y [In(x² + 2)²1³ 3. y = xsex

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Q: SOLVE THE VOLUTION OF THE #F ㄜㄊ y" ty= g(t) = {1, 0≤ t <317 0₁ 773 1 J 9 (₁) = 0 9' (0) = 1

A: Laplace transform of the differential equation

Q: 3. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A: Consider the given position function. st=-t3+3t2-6 Find the double derivative of the position vector…

Q: The bending moment M of the beam is given by -w(l – x) where w is a constant Determine of x given M…

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Q: 10. f (x, y) = 1 sec(xy) in(rv)

A: Solution:-

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = ln (x + 2y + 3z)

A: Given, ƒ(x, y, z) = ln (x + 2y + 3z)

Q: dy Suppose dt =ky, where k is constant and y=6 when=0, Also suppose that y=8 when =3, What is the…

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Q: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = 3t² – 30t –…

A: topic - quadratic equations

Q: dz = 2ni to deduce that z+1 Use the fact that (x+1)dx+ydy Sc O (x+1)dy-ydx = 0 and Jc (x+1)²+y² =…

A: Given ∫c1z+1dz=2πi ......(1)we have to prove that ∫c(x+1)dx+ydy(x+1)2+y2=0 and…

Q: The position of a particle moving along the x - axis at time t is given by x(t) = ecos2t, 0<ts . For…

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Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: Let y = /7– 2. Find the differential dy when a = 4 and dæ = 0.4 Find the differential dy when æ = 4…

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Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = yz ln (xy)

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Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry ln² y + yln y)dr + (2x² In y +…

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Q: Q. Find F(s): e6t St2 cosh 4t dt.

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Q: f(t) = e-t sinh(5t) s2+25 s+1 s2+28+26 g2 +25 s2+28+26

A: Given function is f(t) = e-tsinh(5t)

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: The position of a body moving along s-axis at any time 't is given by s(t) = 16t - 12t, then the…

A: The position of a body s(t)=16t3-12t

Q: f(æ) = / t2 – 9 dt 1+ cos? (t) At what value of x does the local max of f(x) occur?

A: Given: For the local maximum value of f(x), we must have f'(x) = 0. Here,…