Consider the integral a = • 9₂ (y) 9₁ (y) 9₁(4) = f(x, y)dxdy b = 64 *** f(x, y) dyda. Sketch the region of integration and change the order of integration. 0 an(૫)

Q: Consider the region B under the graph of y = 3x² + 1, x [1,3], and above the x-axis. Find the area A…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Calculate the Taylor series for 1/x about 1. O 1+ (x + 1)(x-1) ²+ (x+1) ³-... ○1-(x-1) + (x − 1) ²—…

A: We know Taylor series expansion of 1/(1+x) is given by, 1/(1+x)= (1+x)-1= 1-x+x²-x³+x⁴-....

Q: ind the solution of the given initial value problem. y(4) 10y" + 25y" = 0; y (1) = 8+e5, y'(1) = 6…

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Q: The diameter of the base of a circular cylinder is 8 fteet and the elements are inclined to the base…

A: We have to find the volume of the cylinder.

Q: Question (x,y) = (0,0) Let f(x,y)=√+² (x,y)=(0,0) The function is continuous at the point (0, 0) if…

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Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

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Q: - lim x²ln x x->0+

A: Solution of given question is written in below steps.

Q: lim X118 3x³-2x x²+2x+8

A: We can find the limit as below.

Q: Find the derivative of the function f(x) = (3x4-22³ - 10) ³/2 ○ f'(x) = (12x³ – 6x²)° ƒ' (x) = -—-…

A: The given function is f(x)=(3x4-2x3-10)32 We have to find the derivative of the function

Q: Question 1 [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = xy…

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Q: Find a linear equation that expresses the relationship between the temperature in degrees Celsius Ca…

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Q: (b) By using trigonometric substitution, evaluate the following integral √ √F² + 4x + 5d.

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Q: Use the functions below to find the given value. f(x) = x 2 8 g(x) = x³ (g¹¹) (-2) = |

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Q: After receiving his first income, Mr. J invested P20,000 in a bank for his future family. The annual…

A: This question can be solved by applying the concept of compound interest.

Q: b. (1) (x) c. (fog)(x) d. (gof)(x)

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Q: Let f(x) = { 8x6 if x 10 If f(x) is a function which is continuous everywhere, then we must have b=

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Q: 5) (10 ptos) Determine los puntos críticos de ƒ(x) = ²x³ + x² – 2 2x

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Q: L4Q12. Write an explicit formula for the sequence: - 2, 2, 6, 10, ... A.an = - 2 + 4n B.an = - 6 +…

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Q: A manufacturer has been selling 1800 television sets a week at $480 each. A market survey indicates…

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Q: |-2 Evaluate the triple integral ²³ cos (y²) dz dx dy.

A: Here we have to perform triple integration

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: f(x)=4 sin¹+x+√4x²

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Q: (1 + 2.6) ² an = (1 +

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Q: Find the volume of the solid when the region enclosed by the curves y=x², x=1, x=2, y=0 is revolved…

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Q: A happy heat-loving bug is wandering on a hot plate. The temperature at any point on the plate is…

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Q: TL 3. sin²4ycos²2ydy T

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Q: Question 3 Let D denotes the region in the xy-plane bounded by the parabola 2x y = 2x. (a) Sketch…

A: Please see the below picture for detailed solution.

Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate

Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

A: Let x , y, z donate  the length, width and the height of the rectangular box.  Volume of the box is…

Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: Consider the following function: f (x) = -1/2 x^4 +16x^2 -4 Determine f′(x) and f′′(x).…

A: Solve the following

Q: 7. Let C be the portion of the circle x² + y² counterclockwise. (a) (b) Evaluate La xy dy. = 4 from…

A: Let's solve given integral.

Q: L3Q6. If f(x) = 2x – 1 and g(x) = log x, compute (f – g) (x). A.2x – 1 + log x B.2x – 1 – log x

A: Given; f(x) = 2x – 1 and g(x) = log x

Q: 11. Determine the divergence or convergence of the following improper integrals and evaluate if it…

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Q: Calculate the accumulated amount of end-of-month payments of $9,000 made at 5.89% compounded…

A: The given data is: Monthly payement=$9,000Interest rare r=5.89%=0.0589Time t=5 years  Compounded…

Q: Solve the initial value problem. dy do y=0 +y=10 cos 0,0>0, y(x) = 1 THEE

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Q: 26. Graphed below is the function g(x) and a transformation of g(x). Write an equation for the…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: (d) Find the volume of the solids generated by revolving the region in the first quadrant bounded by…

A: We need to find volume.

Q: rticle subject to a force F(x, y) = (-6y, 6x) moves clockwise along the arc of a circle of radius 4…

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Q: Find f   f '''(x) = cos(x),    f(0) = 7,    f '(0) = 6,    f ''(0) = 5

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Q: 7 circle r = cos 6 and circle r = sin 0

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the area inside the inner loop of r = +3 10sinθ

A: Concept: The area inside the loop is given by the formula A=12∫αβr2dθ Where r represents the loop…

Q: Use the Product Rule or Quotient Rule to find the derivative. f(z) = (3x-²+5) (-4x−³+4). ○ f'(z) =…

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Q: The hypotenuse of right triangle is 74 meters long. The difference between the other two sides is 46…

A: We know that for a right triangle , Let hypotenuse is c and other two sides are a and b. Then…

Q: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

Q: What is the area of the region between the curves 3 y = x³ and y = x², from x = -3 to x = -1? Select…

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Q: The area of the surface obtained by rotating the curve y = √√x + 1, for 0 ≤ x ≤ 2, about the x-axis,…

A: Given :

Q: The general term of the sequence is 2 -1 2 -1 2. - 1층글룸금.... 25 3 an = (-1)"+¹ ²1, n ≥ 1 (−1)²+12 n

A: Given :an=-1n+12n