Exact Equations (w³ + wz² – z) dw + (z³ + w²z – w) dz = 0 O (w² + z?)² = 4wz + c O (w? + 2?) = (4wz + c)?

Q: x* – /x dx бу 4

A: integration

Q: Calculate the iterated integral. 36(u – v)³ du dv

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Q: ку — 1 x²y 1 dx dy = 0 ху?

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Q: Find the shortest distance, d, from the point (4, 0, -4) to the plane x + y + z = 4. d =

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Q: Given: x² dx Find: Formula Se"au o fe"du " du 3 o 1 e"du o fa"du aªdu

A: topic - indefinite integral

Q: 1. The graph of a function f is shown. Verify that f satisfies the hypotheses of Rolle's Theorem on ...

A: Rolle's Theorem Let f(x) be a function that is continuous on [a, b]  and differentiable on (a, b). I...

Q: dx Given: x sinx Find: Formula 2 Jsin u du Jsin u du 02 fcso o fesc u du 2 | csc u du

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Q: 1 dz 4z z z

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Q: Find the equation of the tangent line to the graph of the given function at the given value of x.   ...

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Q: Graph the function f(x)=−4x2f(x)=-4x2 and draw the tangent lines to the graph at points whose x-coor...

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Q: One of the following is an improper integral. Determine which one it is then evaluate it. What is th...

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Q: Evaluate the integral V5+ 12x? - 4x xdx O 1 (2x2 – 3)/5+12x² – 4x4 + 14Arcsin V14(2x² – 3) +C 14 -3)...

A: Using integration of square root of a2 - x2

Q: Apply integration by parts: S udv - S vdu = uV sin2x – cos2x dx sin2x + cos2x

A: Integrate the function (sin2x-cos2x)/(sin2x+cos2x) w.r.t. x 

Q: Use Lagrange multiplier to solve. Max U = x+y+z subject to xyz = 8

A: max U=x+y+z subject to xyz=8

Q: 2. In each of the following, find fyzz, fryx, fxyz. 2. f(x, y, z) = lIn(xyz) + 2² tan¬'(e"Y)

A: I am attaching image so that you understand each and every step. Note:-  2nd subpart is more complex...

Q: Prove that lim X-2 2x2-3x-2 = 5. x-2

A: Topic = Limits

Q: What values of x make 3(x – 5)(x – 12)(x + 5) = 0? If there is more than one answer, enter your answ...

A: Topic = Algebra

Q: Determine the end behavior of the following polynomial functions. (That is, does f(x) increase or de...

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Q: Rewrite the statement in mathematical notation. (Let n be the number of cases of Bangkok flu and t b...

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Q: dx Evaluate 2 -1 O -2 O -0 O O O O

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Q: One of the following is an improper integral. Determine which one it is then evaluate it. What is th...

A: We have to first find improper Integral then we have to evaluate it.

Q: 5. The volume of the solid formed by revolving the region bounded by the curve y = Vcosz, I-ax: from...

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Q: Calculate (1+ cos(y²))dA,where D is the triangular region with vertices(0, 0). (–2 - Vĩ,2· VT) e (0,...

A: Given problem:-

Q: Write an equation for a rational function with the given characteristics. 4, x-intercepts at (-4,0) ...

A: Explained below 

Q: t f be a function that is concave up everywhere. Suppose we would like to use the tangent line at x=...

A: If f is concave up so f''>0 and follow step 2nd . 

Q: Sketch the graph of the given function. Use technology to approximate the intercepts, coordinates of...

A: Given:       f(x) = 4x3 + 6x2-24x+1

Q: sec? x 4 TT dx- Evaluate 1-tan x O 1 O-2 O 2 O-1

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Q: Find fo g, g o f, and g o g. f(x) = 2x, g(x) = x4 %3D (a) fog (b) gof (c) gog

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Q: 1 8. If y = 1+ a) Prove that y' = 0. b) What kind of functions have derivative 0 ? c) You can actual...

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Q: -8 Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....

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Q: V sec3(In x) + sec2(In x) tan(In x) dx Given: 2x Find: du O tan(in x) dx X O tan(In x) dx 2x sec (In...

A: Given:     To determine: expression for du

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,   (−7, 49/2)

A: The objective is to find the equation of the tangent line to the parabola at the given point.

Q: A graphing calculator is recommended. Find the following, correct to two decimal places. (Enter your...

A: topic - functions and derivatives

Q: csc2 Given: lcot2(클x)- 4cot(글x)+ 4 xp - Find: u cot2 4cot x+ 4 cot cot2 4cot X+4 O ca)-2 cot

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Q: dx Evaluate xV x2 - 4 8 프2프4 O O O

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Q: minimum values and saddle point(s) of the function, If you have three-dimensional graphing software,...

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Q: Find the exact location of all the relative and absolute extrema of the function. (Order your answer...

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Q: An object is dropped from a tower, 1936 ft above the ground. The object's height above ground t seco...

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Q: SV + 2) /2 – 3y dy -

A: The detailed solution is given below Thank you 

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x) ...

A: Here ,               We have given a function now we have to solve it by using definition of limit f...

Q: Apply derivatives to determine the critical points of the function ?=?(x−6)².

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Q: Evaluate csc?x cot(cot x) dx. O -In |sin(cot x)| +C O cot(csc?x) + C O - csc?(cot x) + C O In |sin(c...

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Q: 25. f(x) = 1 – V

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, Y...

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Q: Find all solutions to the following first-order differential equation.  Make sure the solution set d...

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Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

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Q: Solve the differential equation with appropriate method. Express final answer equated to y^n. (e.g. ...

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Q: What is the reversed order of integration of dydx ?

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Q: Determine the Laplace Transform of the functions shown and simplify.

A: We can evaluate the Laplace transform of the given function by using the following formula.

Q: Express the general solution in terms of Bessel functions: 4x?y" – 4xy/ + (16x² + 3)y = 0

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