What is the derivative of y = sin (x³ sin (x³ – 3x)?

Q: d- ax d³ y dx3 +6 d²y - 15 dx² Q.2-Solve the differential equation 15-100y = 0 dx

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Q: y=? € x ² y² + (y²) ² = 11 - U

A: see below the solution and calculation

Q: An economy depends on two basic​ products, wheat and oil. To produce 1 metric ton of wheat requires…

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Q: An ice cube is freezing in such a way that the side length s, in inches, is s(t)=t+6, where tis in…

A: Write down the equation of the volume.

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Formula:- Volume of Parallelepiped = [u v w]

Q: Assume a and y are functions of a third variable t. If xy = 30 and 10, find dt 0-6 0-3/1/20 O-12…

A: Here we use the concept of derivatives

Q: If the tangent line to y = f (x) at ( 5, 3) passes through the point (1, - 2), find f' (5)=

A: Given problem:- If the tangent line to y = f (x) at ( 5, 3) passes through the point (1, - 2) Find…

Q: [C (sec 9x + csc 9x)³ dx

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Q: Find a number in [0,1] such that the difference of 1/3 the number from its cube is minimized.…

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Q: Given w = xe¯ª + ln(x²yz³). Determine δω ?х ?w dx 2 = -xe tết xyz³ dw = xe¯* + 1 + 1²/12 8x dw…

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Q: 6. 7. 8. (ex + e + x) dx 24t dt [2(5x) dx

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Q: Find a value of n such that y= x" e satisfies the equation xy' = (x-6)- y. (Use symbolic notation…

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Q: d) y = 21+1 31-2

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Q: Find the area of the region bounded above by y = x³ + 1 and below by y = x + 1. 3 2.5 2 1.5+ 3.5…

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Q: 12. How much work is done by a variable force F(x) = (40 - x)N that moves an object along a straight…

A: Given that, the variable force is Fx=40-x N the interval is 4,20. Note that, the total work done by…

Q: Use the Integral Test to determine whether the series is convergent or divergent. nhe-n n = 1…

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Q: Write the following sets in set-builder notation. There may be more than one correct way to do it.…

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Q: Solve the differential equation x²y"— 6xy'+10y = xº cos(2x) . Linearly inde

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Q: Solve the differential equation d²y dx² - 7+12y = 12x² + 7x + 13.

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Q: C- - 0 x4 (1-√x)5dx

A: we  need substitution method to evaluate given integral

Q: D Question 8 For the function y = (x - 2) Inx what are the two x intercepts, and between the two…

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Q: In sketching y= O None of the choices O y = 1 O x = 1 O No horizontal asymptote (x-1) In z determine…

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Q: Solve the following. 1. Find the volume generated by revolving the first-quadrant area bounded by…

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Q: Given: xIn y + y²z + z² = 8 Find: дх дz -(x + 2y² z) y(y² + 2z) -y ln y x + 2y² z - In y у2 + 2z -у²…

A: Let's find derivative of given function.

Q: Given f(x, y, z) = zey 02 √√3 O 2e² 01-1 √3 O none of the choices 0 0 √3 x sin (3), what is fzz…

A: Differentiate and put the appropriate values.

Q: Let f denote the function if x < 2; 1 f(x) = if x 2. Which of the following is true about f? Of is…

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Q: Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

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Q: Suppose a person is going up in a hot air balloon. The surrounding air temperature in degrees…

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Q: A large tank is partially filled with 100 gallons of fluid in which 30 pounds of salt is dissolved.…

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Q: 6. Find the volume of the solid generated by revolving about the y-axis the region bounded by the…

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Q: The area in the first quadrant under the curve y = e-x is revolved about the x-axis.  Find the…

A: Topic = Volume

Q: d. y""-6y" + 12y' - 8y = 0

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Q: The graph of O the x-axis O the y-axis O None of these O the Origin y = = xe is symmetric with…

A: From the property of the odd function we observe that function is symmetric property.

Q: Give a general solution of the differential equation y"–9 y = −2t cos 3t

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Q: A particle moves back and forth along a straight line. Its position (in meters), relative to the…

A: Find out the total distance travelled during the first 10 seconds.

Q: A=  0 0.3 0.25 0.1     D=  3 4

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Q: Evaluate the surface integral [[ F.ds where F(x, y, z) = (x³ +y³) i+(y³+z³) j+(z³+x³) k S and S is…

A: We will calculate surface integral , use of divergence theorem

Q: 0, -5<z<0 92, 0≤z<1 then 11, 1<x<5 E If f is the Fourier series of g(x) = f(z)- What does f(-5)…

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Q: From the following results, determine whether the function f(z) = 2x+8, 2<8 8 16, = 8. Justify the…

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Q: Q2 (a) Sketch the following function of period 27. f(x)= |x| (-1 ≤ x <n) f(x + 2x) = f(x) (b)…

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Q: Which of the following is TRUE for all? All functions are continuous at all points in its domain.…

A: Given :   Continous and differentiable functions

Q: 4. A plane travels on a bearing of 15° at an air speed of 655 km/h. It encounters a wind blowing at…

A: This question is related to vector addition, we will solve it using given information.

Q: Find the area of the region bounded above by y = x2 + 8 and below by y = 4. 10- 4 2 X -10 8 6 4/-2…

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Q: c - [² x ² (1 - √x ) ³dx 0

A: In this question we have to evaluate the Integral.

Q: Find the area of the region bounded above by y = sin(x) and below by y = cos(x 2 1.5 4 0.5+ X

A: Using horizontal /vertical strip

Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3,3] is shown below:…

A: we have given the graphf will be decreasing in itervals where its slope is negativewe can observe…

Q: Question 2 (a) Find the derivative of the function. x3 F(x) = sin(u²) du (b) Find the area of the…

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Q: 4. Three collinear vectors, a, b, and c, are such that à = 2²/b b and à = 1/2c. (a) Determine…

A: The objective of the question is determine the knowns.

Q: The temperature of a room in degree Celsius is modeled by a differentiable function T(x) where x is…

A: We need to choose correct option.

Q: x²-3 (x-1)² Analyze and sketch the curve given by f(x)=- 2(x-3) (x-1)³ · if y'=—- and y"= 4(x-4)…

A: Given