find the equation of the tangent and thhe to the Pollo wing cunve uhen x = 1 (2x2- Ja)2 normal .

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Q: x dy Q33. Solve the differential equation = 3x dx (a) y =+ ce 5 (b) yà = +ce 5 +ce 5 (c) yš = Vx +…

A: To solve the differential equation xy-23dydx+35y53=3x.

Q: (æ² + 1)² x²ez² 2(x2 + 1) + C x²ez? 2(z² + 1) -ze +C O A Ов 1 2(x2 + 1) cea 2 2(2² + 1) - 2" +C…

A: The given integral is: I=∫x3ex2(x2+1)2dx=∫x2ex2(x2+1)2x dx Substitute x2=u⇒2xdx=du⇒xdx=du2 So,…

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Q: dy = 2/y- 5In|Vy+5| + C Vy+5 (A) True B) False

A: we will use basic integral rules and the method of integration by substitution.

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A: writing given function as x in terms of y

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A: We have to find an expression for the area under the graph of f as a limit.

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A: Given query is to find the integral using substitution method.

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A: Given query is to find the the integral.

Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

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Q: 9 – 4x2 -dx Evaluate: x2 (품) (A 9— 4г2 2.x sin- f (x) = +C V9 – 4.x2 - 2 sin- (4) + C 2r В f (x) =…

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Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

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Q: O Yes, Rolle's Theorem can be applied. O No, becausef is not continuous on the closed interval (a,…

A: Given query is to find rolle's theorem can be applied or not.

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A: Solve the given

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Q: Plot the set 1,0, on the number line. Round to the nearest tenth where applicable. Answer How to…

A: We can plot the points on the number line as below

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Q: If a rock is dropped from a height of 290 ft, its poistion t seconds after it is dropped until it…

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Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

A: Solving

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Q: Use implicit differentiation to find dy/dx. 13) 2хy - у2 - 1 A) _ у -х B) X - y C)L X - y D) – y - x

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Q: 4 3 2- O 1+ -2 -1 1 2 x 1,

A: Solved below

Q: n(-8)" Use the ratio test to determine whether converges or diverges. п! n=25 (a) Find the ratio of…

A: Here we have to use the ratio test.

Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

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Q: 2. Sketch the region and find the area of the region bounded by y = -x? + 9 and the x-axis.

A: The region is bounded by the curve y=-x2+9=-(x-0)2+9 and the x-axis.

Q: Give an appropriate response. 3) Find the limit of f(x) as x approaches 2 from the left. (-3 if x3…

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Q: S sin°x cos³x dx 1 2 1 sin'x +sin°x - sin'"x + C sin'a +sin'x +sin"x +c B 1 sin'

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Q: YA Y= 5X-x² 2. (4,4) Y= x Find the Alea Of the shaded hegion

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Q: Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. 6s +…

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Q: a* (9x" – 10) | The antiderivative of f (x) = - is F (x) where "a" is equal to %3D 30 A 4 В 1 12 1 D…

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Q: Consider the function f(æ) = 10,/T + 7 on the interval [2, 10]. Find the average or mean slope of…

A: This question can be solved using the concept of mean value theorem.

Q: 3. Let h(x) be a twice-differentiable function with h' (x) <0 and h" (x) <0 for all real numbers x,…

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Q: After appropriate substitution, the integral expression a* (x2 + 4)? dx can be express as (choose 2…

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Q: Let A = (1, -2) and B = (6, 2). Solve for projyA. %3D

A: projBA  implies projection of A on the vector B. projBA =A·BB2 B  ............(1) A·B is dot product…