2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: y=8sin(x)cos(x) ; x=pi/3

A:

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Find an equation of the line tangent to f(x) =3 at x 3. %3D OA. y=xln 3+ (1– 3ln 3) OB. y=27(xln 3 +…

A:

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: Use implicit differentiation to find * az given that yz* + x²z3 = дх = exyz

A:

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

A:

Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

A:

Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

A:

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

A:

Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

A:

Q: o find D7 and 22 by implicit diffeuentiatio Confirm that the results obtained agree with these…

A: Consider  the function fTo find: ∂z∂xWe differentiate it with respect to x, treating y as…

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

A:

Q: If Va + Vy = 11 and y(25) 36, find y'(25) by implicit %3D differentiation.

A:

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: 9. Find dyldx by implicit differentiation: 3x³ – 8y² = 10y .

A: To find the implicit differentiation, we will start by taking d/dx on both sides.

Q: Evaluate f, f,(1-2) L(-dy dx dz

A:

Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

A:

Q: Construct a cubic spline that interpolates sin x at nodes 0, T/2, T, 37/2, 27 (use the true…

A: The given function is fx=sinx and the given node points are x=0,π2,π,3π2,2π. Therefore the given…

Q: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

A:

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: If y = eex the y' - y" + exy' is equal to?

A: The given equation is y=eex

Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

A:

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A:

Q: Determine the indicated (in the attached image) partial derivative of z = x4y5 - cos(x3y2)

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Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

A:

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

A:

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate 9.2 . %3D

A: topic - tangent line approximation note :as per bartleby guidelines we are supposed to answer only…

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: Compute the equation of the tangent line to f (x) = sin(Tx) at x=0.5.

A:

Q: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: If Va + Vy = 6 and y(25) = 1, find y' (25) by implicit differentiation. %3D %3D

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Q: Find the derivative of y(x) = In (7(In(x))* ). %3D (Use symbolic notation and fractions where…

A: Topic = Derivative

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: y' – ey : = sin x

A: In this question, we have given a differential equation y'-ey=sin(x) here, we need to check either…

Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

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Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

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Q: What is the slope of the segment in the slope field for dy/dt= ty + 1 at the point (2, 3)?

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Q: Use implicit differentiation to find az/əx and əz/ðy. x2 + 4y2 + 7z2 = 4 dz ax az

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Q: End fz(3) in terms of the joine pdf of X and Y if

A: From the given information, Let, f(x) be the density function of X. f(y) be the density function of…

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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Q: Confirm the approximations by using the linear approximation at x = 0

A: