Find the general (real-valued) solution of the following differential equations. If an initial condition is given, find the particular solution. Usc the indicated technique/s. (a) 3r 2y (y 2r)y 0 using method of exact equations:

Q: Consider the following function. f(x) = 2x3 - 12x² + 18x – 7 Find the derivative. f'(x) = Find any…

A: The given function is: f(x)=2x3-12x2+18x-7

Q: dx -= In[F(x)]+C• What is f(3) For (x+x³) (x Tan-!x+1) 3 3 -1 3 6. + 3 + + +

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Q: Let r = xI + yj + zk and r= |r|. Find each of the following. (Give your answers in terms of r.) (a)…

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Q: |v|dt. Then find the Find the arc length parameter along the curve from the point where t= 0 by…

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Q: Differentiate the following and simplify: y= log, (sinhe") h(x)=3sinh(1–3x² )cosh(1– 3x² ) 1. 2.…

A: As per bartleby guidelines we only give first question answers.

Q: dx + (1 – x²)cot y dy = 0

A: Given problem :- dx + (1-x2 )cot(y) dy = 0 Find the general solution of given differential equation

Q: 3. Find the area bounded by the given curves. Rubrics: Curve accurately drawn with intercepts…

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Q: C. ta the sum or the values of a and h such that f(x) - 2ax2 1 hr + 3 has a relative extremum at the…

A: 7.   The function f(x)=2ax2+bx+3 has a relative extremum at the point -1,2

Q: Consider the indefinite integral (22 da: (z – 2)* 3)2 This can be transformed into a basic integral…

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: The four figures are graphs of the quadratic surface z = x? + y2. Match each of the four graphs with…

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Q: 2) f(x) =f"(x) 3 x+7

A: Use simple differentiation formula.

Q: Using Integration By Parts,x: x dx = u v– Jv du X sec Svou -tanx - Jsec Find Ex tan 5 2 1. X sec x…

A: The given Integral is: ∫x sec 12x tan 12xdx

Q: x² + x +2 Evaluate x2 - 1 x+1 +C (x- 1)2 (x- 1)2 In- + C x+1 x+1 X+ In- +C (x-1)2 (x- 1)2 x + In- X…

A: Given problem:-

Q: Evaluate the surface integral / F. ds for the given vector field F and the oriented surface S. In…

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Q: x(z + 2y)100 = yz – x; Zy and xz.

A: Given problem:- x(z+2y)100 = yz-x  To find:- Zy and Xz

Q: sin dx 32 cosS 35 4 Ssin +2 +c cos () • 32 cos + C 32 -cos 32 cos + C 7 4 32 cos 35 즐)-Scos()+기+C

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Q: r³ – 4x – 1 = 0 3 | Consider the implicit curve throughout this problem. Find dy/dx and use this to…

A: We can solve as follows

Q: 2x+11 3 1 dx evaluate Consider x² + x-6 dx- x+3 x-2 x+3 X-2 x-2 In +C |x+3 |(x-2)³| In x+3 |x+3 +C…

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Q: -Svau Using Integration By Parts, x Arcsec 3x dx = uv- - Svau- Find uv- x² Arcsec 3x dx V9x2 – 1 o 1…

A: Here we have to solve the integration by using integration by parts.

Q: Find the area: y = sin x, the x-axis, the y-axis and the vertical line x = 2 *

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Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,…

A: We have to find the equation of tangent plane

Q: Sketch the curve y = x* - 6x? and show intercepts, maxima and minima and points of inflection.

A: Follow the procedure given below.

Q: (2х + 3у)dx + (у — х)dy —D 0

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Q: 10. Consider the function f (x) = x³ + 6x2 -36x + 4. Then I. f decreases on (-6, 2) and increases on…

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Q: d d Calculate ri(t) · r2(t)] and rı(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: |x Arcsec 3x dx = uv- -Svau Using Integration By Parts, Find UV- du x2 Arcsec 3x dx x²-1 = x2 Arcsec…

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Q: 8. dx +x2 Integrate:

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Q: In how many ways can the digits in the number 8,400,000 be arranged? ways (Type a whole number.)

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Q: Evaluate the integral (2 + 6) (2? + 6z + 2)*dz by making the substitution u = x² + 6x + 2. + C

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Q: 3. Evaluate the lim(2x – 7). x-4 а. lim(2x — 7) %3D 2 x-4 b. lim(2x – 7) = 1 с. lim(2x - 7) %3D7 x-4…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 3r + cos r Use Squeeze Theorem to evaluate lim V1+r² – 5x°

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Q: Select all that apply: □ (5. 똥) □ (5. 플) O (5. -*) (-5, ) □ (-5. 똥) O (-5, -)

A: Polar

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: Using Integration By Parts, x3 Vx² + 4 dx = u v- -Svau - Svdu- بی تر ر ترا Find UV- 3 1 .x2 (x2 +…

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Q: 3x2+ 8x – 12 3. -dx. Use partial fractions. x3+7x2+ 12x

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Q: /9– x² using Trigonometric Substitution what is dx ? onsider x2 3 sec e de P 3 cos e de O 3 sec e…

A: Topic:- application of integration

Q: cos 2 dx O 32 -cos -5cos2 ()+7] + c 35 32 35 - cos(4)- 32 -cos) +c O 32 COS +C 스4

A: We have to find integral

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the y y = 5 x-x…

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Q: Find 8²-45+13 2

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Q: Evaluate the integral cot5 x csc3x dx O Lesc" x - ese" x + cse" x - c 2 csc' x + 5 글csc3 x + C 1 X +…

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Q: 9- x2 dx using Trigonometric Substitution what is dx ? x2 Consider 3 sec e de 3 sec? e de 3 cos e de…

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Q: 3) y = 2 - 3y; y'

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Q: Compute the given integral. Jac dx +C

A: Solve the integration

Q: dy dx? Find in terms of x and y. x°-y° = -3

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Q: Difference of quotient for 1/(x+4)^2

A: The given function,       1x+42

Q: Find an antiderivative of the function. (Remember to use absolute values where appropriate.) (a)…

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Q: Safari File Edit View History Bookmarks Window Help A docs.google.com Google Docs Untitled document.…

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Q: S2x²-x² + x+2 2x3- x4 + x D |dx find A + B+ C+D· x+1 Consider O 2 O 5 O 4

A: Here is the solution