sin x Let g(x) = 1 ot. Find the derivative d'(x). '2 1+t3 none of the choices cos X 1+ sin3x sin? x 1+ cos x cos? x 1+ sin x sin x 1+ cos³x

Q: (e) Suppose that the functionf is represented by the power series f (x) =1- +(-1)*. - -- +... 2 4 8.…

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Q: Q2/ Fit a second -order polynomial to the data in the following table: 5 1 4 2 Y 2 8 3 4 -1 4 6.

A: We need to find quadratic equation.

Q: а. Consider the functions y = 2u² + 3u and u = x². Find dx b. Find the derivative of the function…

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Q: Q3) Evaluate triple integral f Lx - y²)dz dy dx.

A: The given problem is solved below in detail.

Q: Let f(x) be a differentiable function such that for all x > 1, f(x) > 1 f(x) and f(x) < lim f(x) = 1…

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Q: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

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Q: Find the value of c where lim(x) does not exist for the graph of the function shown below a. none of…

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Q: H.w Pind the ro.t when [!,3} by Disection?

A: We have to find the root using Bisection method.

Q: Solve the D.E dy -(2x /1-y2)dx = 0

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: Evaluate +V7dx 3 Oa.5 +C 2 5 3. Ob.2 3 2 Oc 2 sm +- Ot ast Od +C 3 2 52~

A: Evaluate integral

Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Let's find.

Q: 1. Find the indicated limit or state that is does not exist lim (3x'y- xy³) а. (x,y)→(1,3) b.…

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Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: Find an arc length parametrization r1(8) of r(t) = (sin(t), cos(t), t). r:(s) = (

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Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: Find the coordinates of all points on the curve x^2 -2y^2 = 5xy-33 where the curve has a horizontal…

A: x2-2y2=5xy-33 →(1)Horizontal tangent slope is 0Differentiate (1) w.r.t…

Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.

Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: E. Consider two functions f and g on [0, 7] such that I f(x) dr = 9, g(x) dr = 6, (2) dr = = 4, |…

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Q: We are told that the sand is falling onto the pile at rate of 9 cubic feet per minute. We want to…

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Q: (-1)" x2n+1 En=0 (2n+1)! Given: sin x = for x ER Determine the exact value of the sum Σ (-1)"(2n +…

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Q: Q4) Find plane area inside the polar function r = 2sin E-0) and outside T= sin in-e) in first…

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Q: Evaluate the following limit: (x- 2)2 – 4 | lim If it does not exist enter DNE.

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Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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Q: Express the shaded area of the region shown below by double integrals of order of integration (1)…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: We have to slove differentiable function above question

Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

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Q: Find the area of the triangle with vertices P(1,2, –5), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the…

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Q: Q3) Evaluate triple integral (x - y²)dz dy dx.

A: tripple integral  First we will integrate w.r.t z and then w.r.t. y and then w.r.t. x.

Q: Q5/ Use Linear Regression to fit the following data: 1 4 5 6. Y 4 9 10 10 9 8 3

A: From given data

Q: Find the speed at the given value of t: r(t) = (e4, -9,4t-1),t = 4

A: We know that V(t)=r'(t)Here r(t)=&lt;et-4,-9,4t-1&gt;Differentiate…

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

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Q: Let f(x) be the function 11a - 5x+4. Then the quotient f(8 + h) - f(8) can be simplified to ah + b…

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Q: Given Ax) = - 2 use the first principles definition to find f'(1).

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Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: 1' 1 3 (e) Show that 5 k=1 k k+2

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

Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two…

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Q: For the functionf(x) given below, where x > 0, evaluate lim f(x). X00 f(x) = In(3x' – 3) – In(4x² +…

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Q: dx = x(1 – y) dt dy у(х — 1) dt

A: Solution of the problem as follows

Q: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

Q: 02) Solve the D.E dy - (2x/1-y2)dx 0

A: The given differential equation is dy-2x1-y2dx=0

Q: Determine the general equation of the plane Ω passing through the point P(−5,−4,1) and parallel to…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

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Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

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