Evaluate the following integral. 36 2 x - 36 36 x²-36 2 dx= dx

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Q: Find when 6x² + 3x³y - 2y = 40. dy dx dy dx The slope of the tangent line to this curve at the point…

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Q: An employee's monthly productivity M, in number of units produced, is found to be a function of the…

A: An employee's monthly productivity M, in number of units produced, is found to be  a function of…

Q: Determine the vertex of the parabola whose graph is given below. MMM 6 5 4 S 2 -7-6-5-4-3-2-1, 1 2 3…

A: The graph of the parabola is To determine: The vertex of the parabola.

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Q: Solve the following homogeneous diffe y"-4y'+4y= 0 »._4y"+л²y = 0, y(0) = 2, y'(0) = 0 x²y" - 2xy' +…

A: Given differential equationwhich is clearly a Euler Cauchy DE

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Q: Solve the second order. Dieg - Ý - ý syes 1 39

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Q: Find the values of the other trigonometric functions given the following conditions.  a. sin theta =…

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Q: If lim f(x) = 4 →2 then compute the exact value of x + f(x) lim x→2 Enter your answer as a decimal…

A: The Root Law:The Sum Law:

Q: r(t) = 2t²1 - 4tj + 2t³k (a) r(t) (b) r"(t) (c) r(t)r"(t) (d) r(t) x r"(t)

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Q: The circumference of a sphere was measured to be 78 cm with a possible error of 0.5 cm. (a) Use…

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Q: List the four smallest elements of the set. (Enter your answers as a comma-separated list.) {y|y =…

A: {y|y = x2 − 3, x  integers}

Q: Verify that f(x) = 2x^3 + x^2 − x − 1 satisifies the hypotheses of the Mean Value Theorem on the…

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Q: Use logarithmic differentiation to find the derivative of the function. y = (tan x)8/x 8 -tan(x) tan…

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Q: y′′ − y′ = x The equation has a particular solution of the form y = Ax + B (for some constants A and…

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Q: Solve 12 4x+1 <3

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Q: The table below gives the velocity of a runner at half- second intervals during the first three…

A: Given the table below gives the velocity of a runner at half-second intervals during the first three…

Q: A helicopter gets into difficulty at time t= 0. Its altitude (in meters) is given by…

A: Sorry we can solve only three sub parts.A helicopter gets into difficulty at time t = 0 Its altitude…

Q: p(x) = a + ax + a,x² + ... + 10x?

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Q: The function f is defined by f(x) = x³ −3+4 cos (3x + 2). Use a calculator to find all values of a…

A: f(x)=x3−3+4cos⁡(3x+2)

Q: If a stone is thrown vertically upward from the surface of the moon with a velocity of 8 m/s, its…

A: Given that a stone is thrown vertically upward from the surface of the moon with a velocity of 8…

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: In this question, we will draw the graph of the parametric equation.

Q: 4. For each integer n ≥ 0, define In = [cos" (a) da. (a) Use integration by parts to prove the…

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Q: Use implicit differentiation to find an equation of the tangent line to the ellipse defined by x² +…

A: By using the implicit differentiation to find an equation of the tangent line to theellipse defined…

Q: 4. Se 1+e 2x 5. fe²x sin 3xdx

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Q: The equation has an unbounded solution. y′′ + 4y = sin x true or

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Q: lim √xe-x/2 x → 00

A: L=limx→∞xe−x/2

Q: -4 -3 -2 -1 4 3 2 1 -1 -2 -3 -4 1 2 3 4 20x For the above rational function f( x ) = 3.5r2 +3…

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Q: Find y as a function of a if y(0) = 7, y'(0) = 4, y"(0) = 133. y(x) = y" - 8y" -y + 8y = 0,

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Q: Find the first and second derivatives of the following. 1-4√√x+x³ (a) y = (b) y = 3x²e² Y (c) y = x³…

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Q: Find the area of the region that is enclosed between y = 6x² − x³ + x and y = x² + 7x. Part 1: Where…

A: First draw the both graphs and find the intersection points by equating to each other than integrate…

Q: Solve the equation. 1 27 3x4/5

A: Given,

Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

A: f(x)=x3x3+3;x=1

Q: 0 1 3 2 X f(x) f'(x) -2 -1 2 N 2 133 When x = 0 then D 1 255 324 X 0 3 g(x) 1 2 g'(x) 2 3 -2 0 g(x)…

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Q: Which of the following is/are signified by lim f(x) = ∞? x→a The limit exists and equals infinity.…

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Q: Work of 4 Joules is done in stretching a spring from its natural length to 16 cm beyond its natural…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O-4 and 2…

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Q: Find the derivative of: Type your answer without negative exponents. Simplify completely. 25x 3…

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Q: fe2x sin 3x dx

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Q: 2 p(x) = a₁ + ax + a²₂x² + ... + 10x⁹ = k = 1, 2, 3, ..., 9 •P(---) 10 1 k 00

A: It is a nine degree polynomial whose coefficient of x^9 is 10

Q: Put the following function in the form P(t) = Poekt. P(t) = 110(0.72) NOTE: Round your answer to…

A: If we need it in the form P = P0 ektGiven, the P0 term is there (it is 110)The only thing we need to…

Q: For the vectors u = 37 - 8j + 2k and v=4i - 23 - 4k we have ū × v = 28i + 20j +38k. Select one: O…

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Q: ²-3x. If there is more than one, separate with a comma.

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Q: ind the following limits. -2x³ - 6 x→∞ −5x² - 7x - 8 a. lim -2x³ - 6 x→→∞ −5x² – 7x - 8 b. lim ||

A: Here we will find limit of the given functions, we will find it on putting the x= infinity and -…

Q: Differentiate. dy dx In x y= 12 X ||

A: we need to find out the derivative of the given function.

Q: Find the local maximum of the function f(x), which is given in the graph below. As an ordered pair…

A: Find the local maximum of the function f(x), which is given in the graph below. As an ordered pair…