3- , thei a) E{f,(y\x)} =- exp(- o/27(2-r²) 20ʻ(2-r²)' 1 b) E{f, (x)f;(y)}=- 2.noV4-r

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

A:

Q: Use the Existence and Uniquness Theorem to verify, with initial value (-2,-1): y' = xy2

A: Consider the differential equation y'=xy2 with initial condition -2,-1 Compare the differential…

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

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Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: Issol za 53. f(x) = VxIn x on (0, co) %3D

A: Given: 53.   fx=xlnx,  0,∞

Q: Suppose X1, ..., Xn are iid with PDF f (x | 0) = 40ªx-5. x > 0, where 0 > 0. Find the method of…

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Q: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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Q: .8 Estimate the error if cos t is approximated by 1 2 in the 4! integral cost? -- + - dt.

A:

Q: 1-E-, find x, y from エ+y 4. 3 3.

A: given two matrices are equal. that means, Both matrices have same order, and the corresponding…

Q: 1-у у-т т-li y – m m– l l-y|=0 |m – l 1-у у- y – |

A:

Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: Let C be the shortest path that connects t to ni and I = S. (coshz + 1)dz. Then I=0 1--sinh π+…

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Show that ! fransform fix into It fn, linear "difference equation: equadion: SkH= +1. JKH

A:

Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δt = 0.006t2(0.006 t…

A: Given, δt=0.006t2 Now, we have, at=e∫0tδsds=e∫0t0.006s2ds=e0.003s30t=et3500

Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

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Q: Find 2. dy of 2.

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Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: 2. Prove that f(x) = |x + 1] 1| (−1,0) tangent line at has no

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: A particle is moving with S. H. M. while making an excursion from one point of rest to another, its…

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Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

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Q: Let C be the shortest path that connects 7 to ni and I = f. (coshz + 1)dz. Then --sinh π+ π(1- )…

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: In(8z) Siven f(z) the derivative f'(x) is 8. %3D O 8 8x o 1 O 78z 1 8x 1/8

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Q: I* cos z lim 1³+2

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Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

Q: Suppose f(x, y) = / tan(x) + y and u = (-3,0). Then, Du f(-0.8, 8) =

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

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Q: Compute the following. (a) limz-2i (2z+3)(z-1) z2 – 2z+4 (b) Derivative of (1 – 22)*. - IT/4 (c) S7…

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