Using calculus, find the absolute maximum and absolute minimum of the function f (x) = 6x² − 36x + 2 on the interval [-5, 4]. absolute maximum = absolute minimum = M₂ HW

Q: Suppose that f(5) = 1, f '(5) = 7, g(5) = −5, and g'(5) = 8.Find the following values.

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Q: The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox…

A: dimensions of the Roy and Roger's sandbox : length =  t2  width = t5 height = v2…

Q: Culator. A particle is moving with velocity v(t) = 1²- 9t+18 with distance, s measured in meters,…

A: The objective is to find total distance travelled.

Q: DETAILS ZILLDIFFEQMODAP11 2.5.003.EP. Consider the following homogeneous differential equation. xdx…

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Q: Q3/: Find the area r=1- cose and over the region R that lies inside the cardioid outside the circle…

A: See this solution I below

Q: Find the unit tangent vector T(t) at the point with the given value of the parameter t. 2t r(t) =…

A: In this question, we want to find the tangent unit vector of r(t) at t=0.

Q: for the volume below...if Cylindrical Shell method was used ...What are the limits of integration? *…

A: use cylindrical shell method   V= ∫ab2πrh dx   where r= radius of cylinder             h = height of…

Q: Find for THREE of the following functions: dx *²)+In/cos(x)). 5 2(cos(x)))

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Q: Task 5. What is the domain of the function a) (0, 1) b) (-∞, 1) c) (-∞, 0) U (0, ∞) esin (1/2) y =…

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Q: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: Find for THREE of the following functions: dx 1-y()+In(cos(x)) + √2-y=2(cos(x))*(x)

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Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: To find the coordinates of P and find the equation for the line .

Q: * The following function f(x) = x^4 sinx is odd O neither even O O

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Q: (1+x)*dx X

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Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: Sketch each of the following: . the solid E • the projection of E onto the xy-plane the projection…

A: answer is in next step.

Q: The volume of a solid E is given by 9-1² 9-x²-y² 1.***** 1 dz dy dx -3 JO 0 (a) Sketch each of the…

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Q: If z = y¹ - 4y³ + 4y² - 1, then the set of values of y for which z' equals 0 is A. {0, 1, 2} B.…

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Q: a) Graph the function f(x)=2x-5x + 3. b) Draw a tangent line to the graph at the point whose…

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Q: f sec¹ x dx

A: Integrate the integral sec7x .

Q: Find the average of two numbers (x1, x2) and print" pass "if the average is more than 50 and "not…

A: Given numbers : x1,x2  Average  of number = (x1+x2)/n                 where n=2

Q: 1. g(x) = Sin 39 COS 32 5 ㅈ

A: The objective is to differentiate the equation.

Q: d²y Find for the following function. 2 dx y= (3x² +1) -5 d²y dx² =

A: On solving this we will get

Q: UT 5 4 3 2 1 Find lim f(x) 3 05 2 04 O Does not exist 2

A: Given

Q: Find the arc length of the curve y = 2/3 (x − 1)3/2 on the interval [2,3]

A: Arc length is given by the following formula

Q: Find the solution of each of the following differential equations: a) y'=ye² +2e¹, y(1) = 3 b) 2…

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

Q: 7) lim (cotx +cscx) XIR

A: lim      cotx + cscx x -->π lim      cosx/sinx + 1/sinx x-->π lim      (1 +cosx)/sinx x-->π…

Q: Consider the solid region E inside the sphere x² + y² + z² = 4 and outside the cylinder x² + y² = 1.…

A: This question is based on 3-D geometry.

Q: Find y' y= y" = 3x + 4 2x-3

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the arc length of the curve y = 2/3 (x − 1) raise to 3/2 on the interval [2,3]

A: We have to find the arc length of the given interval [2,3] .

Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ = dx 7x +…

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Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

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Q: 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ − 2x² + 4)

A: In this question, we want to differentiate the given function f(x).

Q: Use Lagrange multipliers z = f(x, y) = x² − xy + y² to find the absolute maximum and minimum values…

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Q: lim f(x) = 9 lim_ g(x) lim_h(x) = 0, X→2 X→2 X→2 find the limits, if they exist. (If an answer does…

A: Topic = Limits

Q: 3 4) Sain ³x cus³x dx 3 a) - + cos²³x (vin³x + ²) + C 2 b) = cos²x (Ain²³x + ²/2 ) + Cc c) - — cos…

A: To evaluate the integral.

Q: 1. Let A = 24 12 -40 20 and consider the linear system = AY. Let Y(t) be the solution 5 What is the…

A: answer is in next step.  i can answer only one  question as per guideline thank you.

Q: Q4: A conical tank with Diameter of (2 m) from the top and (5 m) height. At the bottom of the tank…

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Q: Question 2 Assume is in radians. The angles requested are measured counter-clockwise from the…

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Q: The capacities at which U.S. nuclear power plants are working are shown in table for various years.…

A: The capacities at which U.S. nuclear power plants are working are shown in the table.ft models the…

Q: Example 5: Use double integral to find the are

A: In this question we will use basic concepts of double integration to get the required area bounded…

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: Q6) Use Gauss- Jordan Elimination method to solve the following linear equations. 2X + 2Y = 2…

A: Solving the problem by finding the value of the problem.

Q: WEEK 8 LESSON 3: Finding Circumferenc 0 LEARNING TASK 1 Ma'am Rona, Reese's teacher saw Piolo and…

A: Given Diameter=4m  Radius=2m  Solve the learning task

Q: In this problem, y = c₁e*x+c₂ex is a two-parameter family of solutions of the second-order DE y" - y…

A: The given differential equation is;  y''-y=0, y(-1)=6, y'(-1)=-6.

Q: -9-x²-y² L.**** 1 dz dy dx 0 (a) Sketch each of the following: • the solid E . the projection of E…

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Q: * The following function f(x) = x^4 sinx is odd о neither O O even

A: Replace x with -x

Q: If a person's temperature after x hours of strenuous exercise is T(x) = x³ (7- x²) + 98.6 degrees…

A: We have to calculate the rate of change after 1 hours

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 5x)y², y(0) = 8…

A: Topic = Differential equation