(a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ + 8)*. %3D

Q: Consider the lines x = -1+ 2s х — 5 l1 : 3 - 2 and l2 : y = s 4 -2 z = 5+ s а. Find the coordinates…

A: The three parts of the problem are solved in the next three steps.

Q: z-1 Suppose the symmetric equations of lines l4 and l, are = 2 – y = z and x = -1, = 2 respectively.…

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

Q: On what interval(s) is f(x) increasing? Decreasing? Explain

A: Given the graph of the f'(x)

Q: 15. Determine the coordinate of point C, which lies on the y-axis, if it is equidistant from point A…

A:

Q: Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, - 25, ... Determine the sequence's…

A: Given sequence is -1             4                 -9                16              -25 By…

Q: Find an equation of the sphere whose endpoints of a diameter are (-2,0, 5) and (-1,2, 3).

A: We can find the equation of sphere as below.

Q: Study the diagram on the right. Two circles are shown ( ): Based on the information shown in the…

A: Formula to be used is  Angle= arc/radius

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. (n +…

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Q: a. (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 5.

A: We will solve the integration

Q: For the function f(x)= x3 + ax2 + 2a2x + a, there exists a point of inflection at x = 2. Determine…

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Q: y 10 X -5 5

A: Range is all the possible value of y that is output of  defined x

Q: What are the local extreme values of the function f(x) = x³ – 3x + 2?

A:

Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

A: Let's find.

Q: 4. Let F = (3y cos(3z) + 4z)i+ (3+ sin(3z))j. Use the Fundamental Theorem of Line Integrals to find…

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Q: Find a formula for the nth term of the sequence in terms of n. 2 22 23 24 15 20' 25 30' 35 1 an for…

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Q: The solution set of non-negativity constraints is located at Y-axis Quadrant II 3- QuadrantI X-axis…

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Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

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Q: Given f(x) = 2x + 4, what is the value of (1)? Select the correct response: 1 O 2 O 4

A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, Y, z) = 4.x + 2y + z subject to æ? +…

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Q: Describe the end behavior of the graph of the function f (x) = 5(4)" - 10. For o, type in the word…

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Q: 2. Error Analysis. Writing an exponential function from a graph. • Carefully indicate the errors you…

A: Given problem:-

Q: Evaluate the integral. tan x sec³xdx

A: LetI=∫tanxsec3xdxSubstitute u=sec3xDifferentiate…

Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: 3. xy' =y-xe/x ANS y =-x

A: To find out the solution of the differential equation.

Q: 3. Consider the vector field F(x, y) = (2xy, x² – sin y). Evaluate %3D F. ds where C is the curve…

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Q: Find the Taylor series generated by f at x= a. f(x) = -, 1 a = 3 X (x- 3)" Ο Α Σ 3" OA. n =0 (x –…

A: We have to find the Taylor's series for given function at a=3 . For this all order derivatives of f…

Q: x² – 4 For the function f(x) =- x' +3x – 4 a) Find the equation of the vertical asymptote(s) b)…

A: Solution is here

Q: C hnd the firet order parho derivohve of 32 4 5 1. 2) %3D *y-16y²23+43x %3D h Cs, t) =° E*In ts3) +…

A: Solution is here

Q: d.x | – 2x² + 1 b.

A: To evaluate: I=∫x5x4-2x2+13dx

Q: Consider the function f(x) =2x + 6x? on the interval [1, 3]. Let K ER be such that K = max |f"(x)|.…

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Q: .9

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Q: Evaluate: L-1 1 S2s-9) 2+2. th CamScanner

A: Let's find.

Q: dz dz Draw a dependency diagram and write a chain rule formula for and given the functions below. ds…

A: 1. D  2. D

Q: explain

A: We will check whether fundamental theorem of calculus applies.

Q: 1 an 1 Use the transformation u = 2x+ y, v=x+ 3y to evaluate the given integral for the region R…

A: Given

Q: Given the vector ủ = (2,0,1) (a) Solve for the value of a so that ū and i = (a, 2, a) form a 60…

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Q: Maximize f(x, y) = xy Constraint: x + 9y = 18 kimum of f(x, y) = at (x, y) =

A: Given

Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

A:

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given

Q: Which of the following is true for the graph of Ax) on the interval (0, 2)? (Circle ALL that are…

A: The graph of the function fx

Q: n3 + n? ) Σ 00 (n – 1)! n=1 2n + 3 n2 In n n=1

A:

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = e 2x2 + y? - 8x…

A: To find out all the local maximum, local minimum and saddle points.

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: In cos x (1) lim x→0 tan x2

A: Let's find.

Q: 27T 3. x y2 and x + y = 2 is revolved about y = 1. (Answer: C. u.) 2

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Q: (b) ( )Find the inverse Laplace transform 2 2s +3 (s - 5)(s +3) 82 +4

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Q: By considering different paths of approach, show that the function below has no limit as…

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Q: 9.x (vi) S dx. x2+15 da. u =

A: Let I=∫9xx2+15dxTake the constant outI=9·∫1x2+15dxSubstitute u=x15.Differentiate…

Q: In a race, Molly starts running from rest at a constant acceleration of 3 m/s. She is running in a…

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Q: Solve the following initial value problem. f′′(x)=−36x^2−18x−4,f′(−1)=13,f(−1)=−35

A: To solve the initial value problem.