Given that (-1, 3) is a stationary point of the function f (x, y) = -x3 + x2 + 2xy+ y² – x – 4y. | Determine that nature of this stationary point. None of the above O Local Minimum Local Maximum Saddle Point

Q: The volume of. a cube decreases at a rate of 0.5 ft?/min. what is the rate of change of the side len...

A: Application of derivative

Q: 3. The chemists say that between 0 C and 30 C, the volume V (in cubic cm) of 1 kg of water at temper...

A: The temperature at which water has minimum volume is T = 3.967°C

Q: 4. State the domain and range of the following functions. a) у%3D 5х —4 b) y= Vx-x c) ((x,y)ly = vx²...

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Q: Find dx | cos (P) dt y = dx I3D

A: NOTE: Refresh your page if you can't see any equations. . use the integration rule 

Q: Sketch the region enclosed by the given curves. y = tan(9x), y = 2 sin(9x), - π/27<x< π/27 y y 3 3- ...

A: Here, to sketch the region bounded by the curves y=tan (9x) &amp; y=2sin(9x), -π27≤x≤π27

Q: Find the area of the shaded region. y 20 (1, 7e) 15 y = 7e* 10 5 y=7xe* X -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10...

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the ...

Q: Find the inverse of the given matrix and verify if [A][A]-1 = [A]=1[A] = [1]: [25 5 [A] = |10 4 8 16...

A: Here, the given matrix is: A=25541051681222 First of all, find the inverse of the matrix.

Q: 8. A company is increasing production of oven mitts at the rate of 4 per day. All oven mitts that ar...

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Q: S(2y + 3)?/ y+ 2 dy

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Q: Find what value of c does L dx = 1 ? x4 Answer:

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Q: 2t es the given condition; r' (t) =i+ te-t"j - =k;r(0) = i %3D t2+1 Vt2+4

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Q: A discrete random variable X has the following probability distribution: 3 4. 1 2 P(X) y 9 1. Find y...

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Q: How much work is done lifting a 10 pound object from the ground to the top of a 30 foot building if ...

A: Here, elementary work is: dw=(2.5y+10)dy

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

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Q: Find the total area of the shaded regions. The area is (Simplify your answer.) Ay 6- +2,4) 4 (2,4) j...

A: Here,, the region is bounded by the curve y=x4-3x2 &amp; y=x2 Now, the area bounded in the first-fou...

Q: Solve the following equation for x. log(4x+170) = 2

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Q: 3. x/1+x° 1 dx (use trigonometric substitution)

A: sec2θ -tan2θ =1 ∫cosec(θ) dθ = 12lncos θ-1cos θ+1+C

Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Given problem:- If a cup of coffee has temperature 100 degrees  °C in a room where the ambient air t...

Q: • Solve the separated functions when (i) k = 0 (ii) k #0 a²x kX(x) = 0 a2x2 %3D

A: For (i), k=0.     ∂2X∂x2-kX=0⇒∂2X∂x2=0Integrating once,⇒∂X∂x=c1Integrating again,⇒X=c1x+c2

Q: Question 2 We consider compound interest with a nominal annual rate r compounded n times per year. T...

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Q: Consider the given function and the given interval. f(x) = (x - 7)2, [6, 9] (a) Find the average val...

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Q: dt 4e-t – et

A: I =∫dt4e-t - etI =∫et dt4 - e2 tet = uet dt = duI = ∫ du4 - u2

Q: dx 9x2 - 12x-5

A:

Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. ...

A: h(x)=fgx and px=gfx

Q: cos° Vx dx x CsC csc Va

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Q: Determine (in ordered pair) the point of intersection of the lines 2x – 5y = 10 and 3x + 2y = 6.

A: Intersection of two lines- Intersection point will satisfy the equation of both lines .

Q: Evaluate the integral 1- 25 ds VT- 25 ds

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Q: 27. Use the disk method to find the volume of the solid generated by the region bounded by the line ...

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Q: The function f is shown below. What is the value of f(x) dx? Write your answer in simplest form.

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Q: Question 2: Compute the derivative of y = arcsin(cos(arctan(r))).

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Q: e3x (1 – 2e3x)2

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Q: The function f is shown below. What is the value of | f(z) )dx? Write your answer in simplest form. ...

A: Topic:- integration   

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the cu...

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Q: 1. 4x° sec .3 x dx cos Va dx Væ csc Va x2 -dr 2.

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Q: dw V5-e-2w

A: Given,           ∫dw5-e-2w

Q: Find a unit vector u in the direction opposite of (-8,-4, -9). u =

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Q: 15. a, = (-1)" 3n-

A: since we are given with multiple number of questions and our guideline is solve the first question o...

Q: So 4х cos (2x) dx e x COS

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Q: x2 dx J V4x – x²

A: Given:       ∫x24x-x2dx    =∫x24-x-22dx  substitute u=x-2→dudx=1→dx=du                    use x2=u+2...

Q: The form of the partial fraction decomposition of a rational function is given below. 16 – (x² + 10x...

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is ...

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Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer ...

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Q: The point P (2,3) lies on the ellipse 8a² + 2y² = c. Determine the value of c and write the point-sl...

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Q: 36. Adams's Magic Hexagon. In 1957, Clifford W. Adams discovered a magic hexagon in which the sum of...

A: Note: As per our company's guidelines we are supposed to answer the first question only. Kindly aks ...

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the cu...

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Q: The following bar graph shows U.S. math SAT scores as a function of household income.† A bar graph ...

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Q: Factor the difference an+1 a, to show that the given sequence {an} is strictly increasing or strictl...

A: an+1= (n+1)/(16(n+1) +9)        = (n+1)/(16n + 25) an  = n/(16n+9) an+1 - an =(n+1)/(16n + 25) - n/(...

Q: (d) dx a + x (e) 1 da J (a + x)2

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Q: Evaluate O xy°dx + x²dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

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