1. Find the following definite integrals: 1 (a) / 3r*(3x* – 2)5 dæ 1 r2 (b) - 2² – 1 xe dx

Q: 2. y = loga(x³ + 2x – 2) 3. y = In³ (x + sin x) %3D 4. y = tan¬1(3x)

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Q: Find 4小1 机g:f el fof (メ= 区 x = 3x # S 3. f位)EX

A: We have to find the fog gof and fof functions.

Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 5. x = c1coswt + c2 sinwt

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Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

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Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: find the inverse laplace tramsform 3/(s-2)^2+4

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Q: For the function glven below, use algebra to evaluate the limits lim f( メー→+ lim f(x), and limf(x)…

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Q: x'sec'ydy – (1 – 2x²tany)dx = 0 %3D

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 1. y sinx – xy² = c -

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Q: find the derivative dy/dx of the functions xlny+ylnx=1

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Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: To determine whether the given function is homogeneous or not.

Q: Question Select your answer. A function f(x) has a critical number a = c. Which of the following…

A: Recall:  y = f(x) + C C > 0 moves f(x) up C < 0 moves f(x) down   Given P(x)=f(x)±k  Where k…

Q: Determine whether the area of the given unbounded region is finite. If the area is finite find it.…

A: The region is bounded by curves y=1x4 , x=1 and y=0 which is to the right of the vertical line x =1.…

Q: how about the equation of the normal line?

A: Apologies for the inconvenience. Here is the solution for the normal line:   From the original…

Q: Find the slope of the line that is tangent to the graph of f(x)=3x²-2 at P(-3, 25). O -3/25 O 27 O…

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

Q: Evaluate by using homogeneous D.E. 3 (3x? + y) dx – 2xydy = 0 03 In(x2 + y?) + 4 = C O a = C(9x³ +…

A: To evaluate by using homogeneous D.E.33x2+y2 dx-2xy dy=0

Q: Integral Calculus: Integration by Parts (Original method

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Q: 1 dx V16 – x²

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Q: Find the orthogonal trajectories of the given family of curves. Draw a few representative curves of…

A: We need to find orthogonal trajectory.

Q: ind cylindrical coordinates of the point with rectangular coordinates (3, –3, –7).

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Q: Funetion Values. Find Re f. and Im fand their values at the given point z. f) = 1/1-2) at 1- i 2) at…

A: Since we have the function                                             fz=11-z then we have to find…

Q: A mass that weighs 8 lb stretches a spring 48 in. The system is acted on by an external force of 8…

A: Given

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. x =…

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Q: sin 2x (1 - 2 cos 2x)? dx 6.

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Q: Question Select your answer. A ball is thrown vertically upward. Its height h feet after t seconds…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S (In x)?dx

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Q: Let f be a continuous function on [a, b]. Which of the following statements is false A If k is a…

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Q: 5. The solid below, known as Gabriel's Horn, is generated by rotating the graph of y = ! about the…

A: To find out the volume of Gabriel's Horn.

Q: (b) Draw the graphs of the solution and of the forcing function; explain how they are related. [1, 0…

A: Given

Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

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Q: Arectangular bin 4 feet long. 3 feet wide, and 2 feet high is solidly packed with bricks whose…

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Q: Integrating Factor by Inspection: (1) y(x² + y² – 1)dx + x(x² + y² + 1)dy = 0

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Q: Determine whether u and v are orthogonal, parallel, or neither. u =j + 8k v = i - 6j - k

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

Q: uantity of cookies sold when the price per cookie, in cents, is x. Use this information to answer…

A: Since we are given with the multiple number subpart answered according to the guidelines

Q: Solve through Bernoulli's Equation: * - y = xy O y-l +x – 1 = ce¯* O y + x – 1 = ce"

A: The standard form of Bernoulli's equation is: dydx+Py=Qyn Where; P & Q is the function of x.…

Q: 4. Find the equation of the tangent to h(x) = x´sin(2x) at x = 1 [no unit circle needed]

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Q: The thermometer reading 700F is placed in an oven preheated to a constant temperature. After 1⁄2…

A: Given problem:- The thermometer reading 700F is placed in an oven preheated to a constant…

Q: Find the open intervals where the function graphed below is a) increasing, or b) decreasing. 10- 10…

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Q: 3 Given y = (1– V2x)°; Find dy/dx O dy :-3(1 – v22)? de O (E) None of the choices O dy 3(1 – V22)°…

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Q: Determine the maximum volume of a cylinder that can be inscribed in a sphere with radius of 10cm.…

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Q: S 3xe*dx

A: Given problem :- ∫ 3xex/2 dx

Q: In trigonometric substitution where the integral involves va? + u², what must be the value of the…

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Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: Which of the following is not equivalent to sin 0?

A: We are asked to find which is not equivalent to sinθ

Q: dy Find for the following expressions: dx a) y = x5 In(3x) b) y = 2 cos (;+ 2x*) Зx2 + 7х + cos (x)…

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Q: x = y² – y, x = y – y² |

A: The solution is given in the next step.

Q: Consider the figures below. (1) (2) 5- 4. Use the rectangles in each graph to approximate the area…

A: Solution is here