Evaluate the following integrals, which have irreducible quadratic factors. 207. S 208. 2 (x − 4)(x² + 2x + 6) لا 2 X √73-2²² + 4x-4d² X 2 -dx 3x16

Q: Evaluate the integral [²(3x² - 2x + 5) d.

A: The given integral is 3x3-2x+5, limit from 0 to 2.

Q: For the following set of variables, find all the relevant second derivatives. In all cases, find…

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Q: 2-4 - 10 i. What is the domain of g? b. Suppose g(z) ii. What is the range of g? Preview Preview no…

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Q: Find the total area between the x-axis and the curve f(x)=√x-1 between x = -8 and x = 8. O O a.) 15…

A: The given curve is f(x)=x3-1 between the x=-8 to x=8   We have to find the area of the curve…

Q: 1 ¹/ de by first rewriting the denominator as a single trigonometric function. cos + sin 0 3. Find

A: We need to find out the integration.

Q: Equations of Order One: Separation of Variables Obtain the general solution of the equation…

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Q: Use a definite integral to find an expression that represents the area of the region between the…

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Q: = (2, -1) and v= (-2,3). Sketch u and v. Then sketch (show how the vectors are adding up) and…

A: Given, u=2,-1,v=-2,3

Q: The solution of a certain differential equation is of the form where a and b are constants. The…

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Q: Find the transform of the given function by use of a table. f(t) = 3e-4t sin 5t A B C D E F (s) =…

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Q: Suppose that lim g(h) = L. h-0 a) Explain why lim g(ah) = L for any constant a 0. h→0 If we assume…

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Q: x) = C 5x² tan r sec x find

A: We have to derivative of given function

Q: Solve for a in terms of k. log₂x + log₂ (x + 10) = k.

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Q: Consider the helix r(t) = (cos(-2t), sin(-2t), -4t). Compute, at t = 7: A. The unit tangent vector T…

A: We can find unit tangent , normal , binormal vector and Curvature .

Q: -1 [cos'x {√(1-x²)}] _dx log. { 1 + ( 1+ sin (2x√(1-x²)) (2)} TT

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Q: Write out the form of the partial fraction decomposition of the function (See Example). Do not…

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Q: 8. f(x) = 3x - 1 f(x) = f(1) x - 1

A: The objective is to solve the above expression.

Q: The given limit represents the derivative of a function y = f(x) at x = a. Find f(x) and a. lim [5(8…

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Q: Find an equation of the tangent line to the graph of f at the given point. 2 1x) = x + ² (1-³) f(x)…

A: The objective is to find the equation of tangent line.

Q: 297. Consider point C(-3, 2, 4) and the plane of equation 2x + 4y - 3z = 8. Find the radius of the…

A: I am attaching image so that you understand each and every step.

Q: Graph the derivative of the function graphed on the right. Choose the correct graph below. OA. in…

A: Graph the derivative of the function graphed on the right.

Q: 203. 1를 2-xdx 2 x² + x xx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Using the position equation of a particle, s(t) following: a) The velocity equation: v(t) = = b) The…

A: Using the position equation of a particle, st=3t3-63t2+405t+20 and t≥0, to determine the following:…

Q: Consider the following limit statement: lim (2x-6)=8 x+7 Find the corresponding value of ō when & =…

A: Condsider the following limit statement: limx→7 2x-6=8To find the corresponding value of δ when…

Q: Find the equation of the curve, if at any point on the curve y'' = 4x - sin 2x and that (π/2, 0) is…

A: Topic:- algebra and application of integration

Q: domain is all real numbers. global maximum at t = global minimum at t = (Enter none if there is no…

A: Topic:- application of derivatives

Q: Show that the function is increasing on the given open interval. (Enter your answers as a…

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Q: dy dt y = sin (tan (9t – 1)) Find dy dt

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Q: lim y³-y y+1 y2 – 1

A: Evaluate the limit limy→1y3-yy2-1

Q: K Find the equation of the line tangent to the graph of f at the indicated value of x. f(x)=8-9 Inx;…

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Q: (a) (b) (c) dy (2x-5)² = dx y dy=3x²(y-1) dx dy_y+2 = dx x+1

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

Q: Find the derivative of y = 5x²sec 1(2x-3). O y'= 10x sec-¹(2x-3) + O y'= 10x sec-¹(2x-3) + O y'=…

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Q: integral of X^3*sqrt(x^2-4) (trig sub)

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Q: Consider the function f(x)= Evaluate lim f(x) and lim f(x). x → 2- X→ 2+ O O lim f(x) = 13 x → 2-…

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Q: Gravel is falling on a conical pile at the rate of 32- min 1 If the radius of the pile is always the…

A: Let the radius of pile be:  r Let the height of the pile be:  h

Q: მე Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2√√2, 4 ) 80 1 where…

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Q: f(3x² − 4x+6) dx ; y = 10 if x = 1. Solve for the constant of integration. Given

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let f(x)=x²-2x on [-5, 1]. Use the IVT to determine if there is a solution to f(x) = 15 in the…

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Q: Consider the function f(x)=√x near x = -1. Find the linear approximation error when using the linear…

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Q: Consider the following equations. f(x) = x² + 2 g(x) = x + 2 Sketch the region bounded by the graphs…

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Q: Question 5. Find an equation of the plane that is parallel to the line of intersection of the planes…

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Q: Determine the x-coordinate(s) of any relative extrema and (1) inflection points of the function y=x…

A: The function is given by y = x2lnx4 To evaluate: The x-coordinate(s) of any relative extrema and…

Q: A particle moves along the x-axis so that at any time t > 0 its position is given by a (t) = (at)²,…

A: Given the position of a particle is  x(t)=12(a−t)2

Q: e [x² uate cos 3x dx.

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Q: 1. Use the Second Derivatives Test to find all the relative extrema and saddle points of f(x, y) =…

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Q: Find the transform of the given function by use of a table. f(t) = 4 + -4t cos 39 t

A: Concept: Laplace transformation: Differential equations can be solved using the Laplace…

Q: Find the derivative dy/dx by implicit differentiation xsiny + ysinx = 1 *Note: please use…

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Q: large tank is filled to capacity with 300 gallons of pure water. Brine containing 4 pounds of salt…

A: we will  find the required.

Q: Find the value of the derivative (if it exists) of f(x) = (x+3)³ at the indicated extremum. Select…

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Q: Solve the differential equation below, when x = ; y = -4. 2 dy dx 5e cosx. If y(37) = a; find the…

A: I have appended the formula used in the solution part of the question