4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the tangent plane to S at the point (E, 1,). 6

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A: This question can be solved using the concept of integration by substitution.

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A: Given u=x2   & dv=cosx dx∫x2 cosx dx  

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A:

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A: find limit

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A:

Q: Find dy/dx by implicit differentiation. 4. x²- 2xy + y = c 5. x'y + xy² =3x 6. y +x°y =1+ ye?

A: This question is based on differentiating equation both side with respect to x.

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A:

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A:

Q: ☺ Find tue indefinile intgrel. cos (5@] do

A: ∫un du = un+1n+1+C ; where, 'C' is an integration constant.

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A:

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A:

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A: Since, the student has clearly mentioned to solve question number (3), so we are solving only questi...

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A:

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A: logarithmic problem

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A:

Q: y' + 3y = 5e2x – 6; y(0) = 2

A: since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: 2.) Find 1st derivative of y = e-'In (x-1)

A:

Q: +o0 (-1)" n (a) ► n! n=1 1 (b) E -3 n - -n n=1

A: Find the limit of the given functions at infinity

Q: SHOW YOUR SOLUTIONS. I. Eliminate the arbitrary constants. 3. x = c, cos wt + c2 sin wt ,w is a para...

A: topic - differential equations

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A:

Q: f(x) =a= 2 3. %3D THE IA

A:

Q: Evaluate the integral by changing to cylindrical coordinates. V 16 - x2 16 - x2 - y2 x² + y? dz dy d...

A:

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A:

Q: Given the systems of ODE below with given conditions x(0) = 1 and y(0) = 2. dy + 2x dt dx et, 2y = 1...

A: First we find value of y in equation 2nd and put in equation 1st .  Follow step 2,3 . 

Q: tan x[cot x – cos x]dx

A: Here we can find the integration as below

Q: Lesson 13 Find the derivative of the following functions. Show your solution. 1. y = x' cos x 2. y s...

A: This can be solved as follows:

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A: The perpendicular distance, ?,between a point ?(?,?,?) and a line with direction vector d→ is given ...

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A:

Q: 3. Let p = 31. Evaluate L3(24).

A:

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A:

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A:

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A:

Q: X- 3/ = 12

A:

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A: Let's find. 

Q: (-1)"+l2nx" Determine the interval of convergence of2. n² +3 n=1

A:

Q: 2.) State one of the two formulas for finding the derivative of a function f(x) that uses limits. Us...

A:

Q: By substitution u = x² + 5x, the definite integral (2x + 5) In (x + 5x) dx becomes Select one: O Non...

A:

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A: Let the container has a base side "x" and height "y"

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A:

Q: Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P. 12ft B The point...

A: Rate of change

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A:

Q: 3. Solve the following equations over all real num V2 sin(-x) + 1 = 0 a. |

A:

Q: B. Use the properties of continuity to determine where each function is continuous. 1. f(x) = 2x*- x...

A:

Q: (a) Graph the function f(x) = 1/x (b) Hence, using translations, reflections etc., graph 1 f(x) = -1...

A: We have to draw the graph of the given functions according to the given information 

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A:

Q: 6) pind ful indefinite integrel. 4 sec (2x) de

A: ∫sec4(8x)dx ∫ sec2(8x)(1+tan2(8x) )dx ∫sec2(8x) + sec2(8x)tan2(8x) dx now assume that tan8x = u du...

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A:

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple quest...

Q: Give the Maclaurin series expansion of f(x) = ln(3 – 2x). Determine its interval of convergence. App...

A:

Q: Find the area of the surface obtained by rotating the curve y = 5x° from x = 0 to x = 9 about the x-...

A: Let's find.