Let u(x) = sin(x) and v(x) = x20 and f(x): u'(x) = v'(x) = f' = u'v - uv' v² = u(x) v(x)

Q: 1. Let v, w be any two vectors. Prove that ||v + w||² - ||v − w||² = 4v. w W (Hint: Use properties…

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 3. A piece of wire 10 meters long is cut into two pieces. One piece is bent into a square and the…

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Q: Evaluate the following integral, where R is bounded by x = 1, y = 2x + 4, and y=-x-2. SS₂² dA R

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Q: A curve is represented by the equation 4y³ + xy - 5x + 4 = 0. Part A: Determine Part B: Evaluate dy…

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Q: Evaluate the integral. (Use C for the constant of integration.) | √₁³²-2² 49 - x² X dx

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Q: Use l'Hôpital's Rule to find the limit. lim X-0 2 8x² cos (x) - 1 8x² 2 Xcos (x)-1 (Type an exact…

A: Given query is to find the limit of the expression.

Q: Use concepts learned in this module to complete this problem set: particle motion, applications…

A: Solve for the limit

Q: Find the derivative of the function. 9√20-³ Select one: OA. -31² OB. √20-3 OD. 1 2√√20-312 OC.…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If f(x)= f'(x) = f'(4) = = 3 tan x X " then

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Q: 8)In the following questions, determine the behavior of h(x)=7x3+6x−x3+10x.

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Q: 4. Solve the given integral |(2* − xe*")xdx 2 a. 2x² C. In 2 3ex³ + C 4x² +3ex³ In 2 + C 2x² 2 ln 2…

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Q: Consider f(x)=x^3−3x^2−9x+4 Note:Note: Use round parentheses for your intervals (open interval…

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Q: Find the equations of the normal line to the surface z=3x4y5 at the point (1,1,3).

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Q: 4. y' - (3+anx)y = 1

A: need to find out the general solution of the differential equation.

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

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Q: A political scientist surveys 40 of the current 153 representatives in a state's legislature. What…

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Q: Evaluate the following integral. 4 √2 S 0 dx 16-x²

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Q: [v₁ Arctanz y dy 。 (1 + y)* Ans. In 2+2 (4√3 − 3). Ans. T.

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Q: In Exercises 39-42, write the equation of the hyperbola in standard form. 39. 3x - 4y² = 12

A: hyperbola is given that  3x2 -4y2 = 12 this is the question of the equation of geometry we have to…

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

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Q: I → Question 2: Are the limits of these functions defined as a too? (please take this opportunity to…

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Q: Use Fubini's Theorem to evaluate the double integral ſf f(x, y) dA, where f(x, y) = −3x − 4xy – 9y²…

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Q: 60. Show that the curve y = 1 + x 1+x² has three points of inflection and they all lie on one…

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Q: A graph is defined by the equation y²(2-x) = x³. Part A: Find dy Part B: Find the equation of the…

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Q: Find an arc length parameterization of a helix of height 20cm that makes 4 full roations over a…

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Q: Complete the following probability distribution table and then calculate the stated probabilities.…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: We can solve this as follows:

Q: Consider the series 1 1 1 1+ + + 6 36 216 a. What type of series is this? Select an answer b. If…

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Q: Find the indefinite integral. (Use C for the constant of integration.) sin³ 50 √ cos 50 dº X

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Q: The function f(x) has a domain of (-∞, ∞) and a second derivative given by the following. F"(x) =…

A: Topic = Derivative

Q: Find the maximum and minimum values of the function g(0) = 30 - 4 sin(0) on the interval [0, π]…

A: To find the minimum and maximum values of the function.

Q: Find the equation (in terms of xx) of the line through the points (-1,4) and (2,-5) answer is -3x+1

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Q: Consider the function f(x) = = function on this interval. 1 on the interval [4, 7]. Find the average…

A: To use the mean value of theorem for the given function

Q: c) Describe the set of all 7. For a function f:A → B, the statement "f is surjective" is defined by…

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

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Q: f(x)=x-x+2x-4

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 2…

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Q: Evaluate each expression using the values given in the table below. -7 -5 -3 -1 -5 9 -3 3 -5 X f(x)…

A: here is table given  we find the function value from the table  a) f(g(-1)) = ? g(-1) = -5 f(g(-1))…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

A: To determine whether the given sequence converges or diverges. If it converges, then to find the…

Q: A bank features a savings account that has an annual percentage rate of r 3.3% with interest =…

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Q: Analyze the following rational function: f(x) 5+2x² 2 x -x - Include the following: 2 • Identify the…

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Q: The graph of a function f is shown below. 1 Suppose the function g is defined as g(x) f(x) =, we'll…

A: Note: - According to the company policy we can attempt only three subparts of a question so please…

Q: Differentiate the following functions, giving your answer in a similar form, without negative or…

A: To differentiate the given function.

Q: In cylindrical coordinates, find the volume of the solid S enclosed by the cone and the sphere as…

A: Given : the cone z=r and the upper hemisphere z=2-r2.

Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 12) ² €-8

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Q: O 8 C 48 Use differentials to estimate the change in when x=5 and dx = -1/6. Use this f(x)=√√3x+1 to…

A: we need to use the differentials to estimate the change in f(x).

Q: Part I Directions: Use the following list of words to help you answer the questions below. "Slope",…

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Q: using DESMOS calculator, shade the area that is INSIDE of r = 3 + 3 cos (theta) and OUTSIDE of r =…

A: The objective is to  share the area that is INSIDE of r = 3 + 3 cos (theta) and OUTSIDE of r = 3.…

Q: h(x, y) = In In (1/2¹)

A: Find below the given  elaborated solution

Q: Suppose the position of an object moving horizontally after t seconds is given by the following…

A: According to bartleby guidelines when student post multiple subpart question then expert must have…