Find the exact value. In 3 0 ³ sech 4 x tanh x dx

Q: Find the general solution of the differential equation y" — y' - 12y -32t + 24t². NOTE: Use t as the…

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Q: Find the general solution of the given second-order differential equation. 30y" 19y' 5y = 0 -…

A: See the details solution in below

Q: x²y (z,y) (0,0) x4 + y² If it exists, find lim Answer: Write DNE of the limit does not exist.

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Q: A population of a small city had 3000 people in the year 2000 and has grown at a rate proportional…

A: In this question, we will use growth topic of differential equations.

Q: Q2) A: By using partial method solve [2x² cos x dx

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Q: Question 3. The parametrization of a curve C is given by r(t) (a) Find r' (π/6). = (sin(t), cos(t),…

A: To find parametric equations of the tangent line to the given curve.

Q: Using the Trapezoidal rule, the approximated value for the integral: g(x) dx, is equal to------ g(1)…

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Q: Find dy/dx if y=2 – x^2.

A: Given query is to find the derivative of the expression.

Q: Q3: A: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

A: We can solve the given differential equation by using the variable separable method.

Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

A: There are two planes on the XY axis.We are at the origin.  Plane X: The first plane is due west of…

Q: The following information is given. f(3) = 5, f(5)= 3, 11. (a) Find H'(3) if H(x) = g(f(x)). 11. (b)…

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Q: Using the Limit Laws, find limt→0 t2+9−3t2. Do not use L'Hospital's Rule.

A: By using the Limit Laws, to find limt→0 t2+9-3t2.

Q: [sin x √9+ cos² rdr

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Q: Maximizing the Volume of a Box An open-top box is to be made from a 30 in. by 40 in. piece of…

A: Let's solve given maximizing volume of a box problem.

Q: P/ find the slope and y-interceft of the line. 8x+59=20

A: In this question we have to find the slope and y-intercept of the line.

Q: @)X = y² + 1₁ x = 0, y = -1 y = 2 The appropriate integrand to find the volume of the solid…

A: Solution is given below:

Q: Evaluate f 10x(x² the following antiderivatives + 5) 7dx

A: The given integral is;  10x(x2+5)7.

Q: 1. Equation of the plane passing through the points A, B, and C. 2. Equation of the straight line…

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Q: Find the average value of the function f(x) = over the interval [0, 6] and find c such that f (c)…

A: We have to solve average value

Q: car traveling at 45 ft/sec decelerates at a constant 7 feet per second per second. How many feet…

A: Given initial velocity (u)=45 ft/secFinal velocity, as brakes are applied (V)=0Acceleration=-7…

Q: X f(x) g(x) -2 5 1 -1 2 3 0 4 1 -2 2 -4 -3 -6 -1 f'(x) -4 -2 1 5 -5 g'(x) -1 3 -3 4 2

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Q: 0. The equation 7(x) = 40cos(x-10)] + 160 describes how an element in a fur cyclically, where x is…

A: topic:- function

Q: Find the general solution of the following differential equation. y" + 5y +6y=0 NOTE: Use c₁ and ca…

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Q: Q ssosiee ※ dy nolaeV DOY MEMedua s x24

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Q: Find the indicated limits, noting L'Hôpital's Rule wherever it is used. lim (1-ª)* (constant a)

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Q: Find the area of the region bounded by the curves, x = −6 ,  x = 6 , the x−axis  and the parabola…

A: Follow the procedure given below.

Q: a. Use limits to find the derivative function f′ for the function f. b. Evaluate f′(a) for the given…

A: The given function,    fs=5s3+3s, a=-3

Q: Compute the double integral ff(6zy2 +12z³y + 4y) dx dy with R= 3,5 z [1,2].

A: See this solution in below.

Q: 11. Integral sin³ R cos R dR

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Q: The following information is given. f(3) = 5, f(3) = -2, g(3)=2, g(3) = 7 f(5)=3, f'(5)=-1,…

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Q: Given f(x) = 3x+8, (a) Find f(x+h) and simplify. (b) Find f(x+h)-f(x) h Part: 0 / 2 Part 1 of 2 (a)…

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Q: Given the functions: f(x)=x²³-8x g(x) = √2x h(x) = 6x+7 Evaluate the function h (f(x)) for x = 3.…

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Q: Q3// 1. Sketch the region D and Evaluate: [ f(x+y) dA Where D, is the triangle region region in the…

A: Let's solve given double integration.

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: To find volume V of the body formed by revolving the given region .

Q: 8. y = In (In (In x))

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Q: 18. Two cars start moving from the same point. One travels south at 60 mi/h and the other travels…

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Q: A region bounded by f(x) = 3 − x, y = 0, and x = 0 is shown below. Find the volume of the solid…

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Q: sin r√9+ cos² rdx

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Q: ○y-3 = cx6 + 3²

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Q: 1. Find the area bounded by the curves between the curve y=1+x and the line y-1 x

A: area between curve

Q: r = 7e0.70 ¬ the interval 0 ≤ 0 ≤ 1 and the straight line egment between its ends. -ea =

A:

Q: Find the location and value of each local extremum for the function. 28) + -3 3 -4 -M

A: To find location and value of each local extremum of given function.

Q: For the function f, given below, find the antiderivative F that satisfies F(1) = 0. f(x)=x² - 4x…

A: Given :f(x)=x4-4x-3+3

Q: Find the integral of the following indefinite integral equations: Jx dx / (5 + 9x4) Jx dx/v(16-9x4

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Q: Use the properties of the definite integral to express the definite integral of ƒ (x) = 6x³ − 4x² +…

A: Given :f(x)=6x3-4x2+2x-3interval [ 1, 3 ]

Q: a. Set up an integral for the length of the curve. b. Graph the curve to see what it looks like. c.…

A: Explanation of the answer is as follows

Q: (b) Using implicit differentiation Find the derivative of 1. y³ + 3x²y = 13 with respect to x and…

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Q: x² - xy (x,y) (0,0) √√√√y If it exists, find lim Answer: .Write DNE of the limit does not exist.

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Q: Evaluate the antiderivatives. 2x dx 5 S

A: ∫2xdx/5 ∫axdx = ax/lna here a =2

Q: A manufacture has been selling 1600 television sets a week at $540 each. A market survey indicates…

A: (a) Here x is the number of television sets sold per week and p(x) is the corresponding price in…