I. Use Lagrange multipliers to find the minimum and maximum values of f(x, y) = x + the restriction that 2x² + 3y² = 14. II. Evaluate x² cos 3x dx.

Q: Given that g'(x) = 21x²-17 and g(2) = 23, find g(x). g(x) =

A: Solution:-

Q: Consider the following functions. f(x) = 4x + 6, g(x) = 5x - 1 Find (fog)(x). Find the domain of…

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Q: 4. An object is moved along the line from the point (1, 2, 1) into the origin (distance is in…

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Q: Direction : Write the expresion in alebragic form  (9) sin(arc sec x

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Q: If 2 is a differentiable function of x and y satisfying the equation sın (x²z + y²) + 2x³=y2²+2,…

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Q: Find the derivative of the function. 3 5)³ - (₁ y = 8x²-5 4-X

A: y = (8x2 -5/4-x)3  we have to find dy/dx here we use chain rule and make differentiation d(u/v)dx =…

Q: Find the inverse Laplace transforms of the following: 7 S-4 (a) Ans: 5 3 + 1 16 + 7 641 144

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Q: f(x)=x^3(x+3) *differentiate the function

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Q: ам Given the D.E. (3x²+2y²) dx + (4xy + 6y²) dy, its av and ƏN dr are both equal to while the…

A: see below the answer and calculation

Q: Given the demand equation p + (x/5) = 40, where p represents the price in dollars and x the number…

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Q: (b) Find (f ¹)'(1) if f(x) = x² +5 sin " + cos2. (TTX) (X)

A: Solution to find the value of derivative of inverse of f(x) at x = 1 is as follow

Q: 1. y=x²(x-1) at the point (2,8).

A: find slope Given point ( 2 , 8 ) for x = 2

Q: direction:  find the derviative  (10)  y=in(x^2 +4)-1/2  arctan x/2

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Q: Use vector notation to describe the points that lie in the given configuration. (Let s and t be…

A: Given that  The plane spanned by.  v1 = (5, 6, 0) and v2 = (0, 5, 6)   To find :- The vector…

Q: 12. Determine the equation of the line tangent to the curve y = 4 = 4(x + 2)²; at the point (4,36).…

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Q: 6. y+y==xyiy==2 ©

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Q: Find the (a) velocity, (b) acceleration, and (c) speed of a particle with the given position…

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) =…

A: Understanding of function and how to calculate its derivative is required in order to solve this…

Q: Let f(x,y) = 4√x+²³+ 4y + ex 1. Use local linear approximation to estimate. 4√ (0.160.9) ³+ 4(09) +…

A: Let fx, y=4xy2+4y+exy By using the local linear approximation to estimate the following…

Q: Find an arc length parametrization of r(t)=⟨e^t*sin(t),e^t*cos(t),9e^t⟩

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Q: If h(2) = 3 and h'(2) = −8, find. d/dx(h(x)/x) x=2

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Q: The population of a town t years after the beginning of the year 2000 is given by P(t) = 5386 e…

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

Q: 3. A certain bacterial culture grows at a rate proportional to the number of bacteria present. If…

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Q: Solve the following system of equations using Gaussian elimination method. If there are no…

A: The given system of linear equations, 5x-6y-6z=2-6x-8y+7z=9-20x+24y+24z=8 We have to find the…

Q: Find the standard form of the equation of a PARABOLA opening to the right such that the endpoints of…

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Q: Differentiate. Don't simplify. 17. f(x) = sin 3x 18. g(x) = (sin 3x)³ 19. h(x) = (sin 3x)³ + 5x…

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Q: 4. G(x) = n x3.4 -5me + p 5. F(x) = ax³ bx² + cx - d 6. f(x) = (3x + 1) (2x7 - x + 2)

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

Q: A business buys a computer system for $12000. The value of the system is depreciating and decreases…

A: We need to find out the value at the end of 3 years.

Q: [We dx = + C

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Q: Consider the following functions. f(x) = ²/₁ g(x) = 3x + 12 Find (fog)(x).

A: Given: f(x)=3x       gx=3x+12

Q: Black pink held a concert in moa arena. the vip ticket sold 15$. Lower box ticket were sold for 10$.…

A: NOTE: Refresh your page if you can't see any equations. . x=number of VIP tickets (each sold for…

Q: determine an equation in factored form for a polynomal function with zeros -1 (order 2) and 3 (order…

A: zeroes -1 (order 2)  :  factor ( x+ 1 )2 3 (order 3)  : factor ( x - 3  )3

Q: 1. Solve the following IVP and find the interval of validity for the solution. y = 5y +e-2xy-2, y(0)…

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Q: Determine if the ff function is of exponential order: show solution 1. t^3 sin2t

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Q: function of x and y sin (x²z + y²) + 2x³ = y2²+2= If 2 is a differentiable satisfying the equation…

A: sinx2z+πy2+2x3=yz2+2 We have to find ∂z∂x at (1, 3, 0)

Q: Compute the first and second derivatives of the functions: 1.) y=tan(x/3) at x = 3

A: Given; y=tan(x/3) at x=3.

Q: For an experiment at the University of Montana, Christopher sends an object down a tube 0.4 meters…

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Q: Find the equation of the line. Use function notation. Horizontal​ line; through(6,-6)

A: Find the equation of the line.  Horizontal​ line; through(6,-6)

Q: A free-falling object falls from rest and has a weight of 89 N. The force due to air resistance (in…

A: Option A is correct the detailed explanation is given below

Q: Use this table about differentiable functions f and g to answer the following. x f(x) | f'(x) g(x)…

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Q: 13limx

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Q: 2x-1 1. At what point/s will the tangent/s to the curve y=- 2x+1 be parallel to the line y-4x+3=0?

A: line  y - 4x +3 = 0   find slope

Q: Evaluate the following integrals a) S √1+x-√1-² dx (Hint: Maybe you need to rationalize the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the derivative of the following functions. Whenever possible, express answer in factored 3.…

A: y=(x^3-6x)(2-4x^3) apply product rule y=uv dydx=udvdx+vdudx

Q: e demand function for math self-help videos is given by 55 -0.2x, and the total cost function to…

A: Given query is to find the marginal profit at x = 20.

Q: Let g be a differentiable function of two variables, with first variable x and second variable y,…

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Q: 3. Determine the following limit (tabulate). sin (t − 1) lim t1 t²+2t - 3 O-1/4 O None of the…

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Q: Given F(r, s, t) = -r(58³ + 7tº), compute: Frst

A: Frst is a third order partial, where we differentiate first with respect to r, then with respect to…

Q: Consider the following. dt ho √ 16+ ² Let t = 4 tan(8) and determine the following. dt t-0-8= t=4-8=…

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Q: Find the equation of the least squares line. Ten students in a graduate program were randomly…

A: The equation of the regression line is y = 3.67 + 0.0313x  Therefore the option (B) is correct.