ду h. ax if cosh(3x²y) = x + In(e*y + 1) i. If fx se and fxx arz find fyyxxx if f = x³y² – – Y əx əx? x+ln(x)

Q: dy Find if y = In x5 + e-cos2x – In e?. dx dy 4 sin x cos x dy 5 es sin²x-cos2 x dx e cos2 x-sin? x…

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Q: Find the Undo pet CWor wa)or the form of a particular solution for the differential eguation:y…

A: Introduction: The method of the undetermined coefficient is a way to find the particular solution of…

Q: If y- In(3 sinh( 3lnx)), then xy'= Select one: O3 coth( 3 Inx) O 3 /sinh( 3 Inx) O 9 coth( 3 Inx) O…

A: Use the Chain-Rule of differentiation to differentiate the function y.

Q: 10 Suppose that " fx) dx and Ax) dx = -5, and "g(x) dx = -1 and g(x) dx = 3. Compute the given…

A: Given,∫04f(x)dx=7∫02f(x)dx=-5∫04g(x)dx=-1∫02g(x)dx=3

Q: Find d if z = log2 y - 6 logs y. In In 64 dz dz dy y In 2 In 5 dy y In 2 In 5 O Option 3 O Option 2…

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Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

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Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: Suppose fhas absolute minimum value m and absolute maximum value M. Between what two values must |…

A: Apply formula for finding correct option

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: 5 (show resulting de) 2xdx - dy=x(xdy - 2ydx) When: x= -3 , y = 1 %3D

A: Differential equation and it's solution

Q: d Prove In Jax| dx In x for any constant a. dx

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Q: 11. Verify that wxy = Wyx for w = e* + x ln y + y ln x

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Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: Suppose that (r, y) = e-v and o(In 2, In 2) = 1. Please use the technique of linear approximation to…

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Q: If y=x² - 4x and x = √2r²+1; find dy dt when t = √2.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: hoaph fumeten nd be fure at label aut least thne f (u) : Su

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Suppose 4x2 + 16y2 = 100, where x and y are functions of t. dy (а) If dt 1 dx find when x = 3 and y…

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Q: 2. If A = f+ g,+ hy s.t f(x.y.z) = e2x, g(x.y.z) = xcosy, h(x. y. z) = log 2z then div A %3D %3D

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Q: Q1) Lind dy/dx of O xe 1o X +3y = 0 2 2sinx cosy=1 9 x = sec!

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

A: Given ∫x2x2+34dx

Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: 1 (5*)csch dy x+1 1. (a) if Find dx x >0. y = 3 (ecosh 5x ) In Vx² +1

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Q: 1 Find the most general antiderivative of the function x3 + 4x

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Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

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Q: 1) Estimate In(1.1) using a linear approximation. 2) Let y = ln(x). Compute dy when x = e and dx =…

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Q: az dz +y =5 ax If z= log ( x+x*y+y° ), Prove that x

A: We can prove this using the rules of partial derivative

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: Solve the initial value problem with piecewise right hand side dy +y = f(x) dæ y(0) = –7 where (5 if…

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Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: a) Find dy/dx ify =(lnx)^x^2 . b)The function f (x) = (ln x)^x^2 is an invertible function (you do…

A: Given y=lnxx2We need to finda dydxbfe and f-1'1

Q: dy y(ln y- In a+1) dx 1 C = -In 1 C = In O Option 2 Option 1 1 C =-In None of the choices O Option 4

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Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: If g(x) = — _*[e'-in(21+1)]dt, find g''(x) . - dx 2 A ex_ (2x + 1)2 B e* - In (2x + 1) 4 с ett (2x +…

A: Given g(x)=ddx∫-2xet-ln(2t+1)dt

Q: Given Z = ye 3r + 2y; where a = ln 2 and y = 2 with possible errors Ax = 0.01 and Ay = 0.03.…

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Q: (2) Differentiate the following w.r.t.x (i) cos (x + a²) (ii) ve+2) + 5 (iii) n log tan (iv) Vtan Vx

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: th 2 Evaluate khe fulawingcartesian integrat by changing theminte equiv alent Pelarintegrals: E 4-y…

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Q: 02 suppose 4xt 9y 36 where x and Q 2 are functions of t if dy =1 Rind dx when x=2 and y = 215 dt y =…

A: Firstly differentiate given equation with respect to 't' and put all the given values and find dydt.