Use the Fundamental Theorem of Calculus to find the derivative of y- " cos t dt t12

Q: (a) What does the equation x² + y´ = 1 represent as a curve in R? (b) What does it represent as a…

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A: P'(x): the rate of change of total profit with respect to the number of tickets sold, x. It is…

Q: whereas Problems 2 and 3 are about determining this information algebraically. A hint for Problem 1:…

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Q: Which of the following is not a possible zero off(x) =2x-5x+ 127 03 5 3

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Q: 1 f(z) = |, + tdt If then f'(x) = 3x^6 f'(-3) = 729

A: fundamental theorem

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Q: x+3 3. Consider the following function. f(x) = x2 a) Find the critical numbers of f, if any. b) Find…

A: The given question has been solved in detail

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Q: Which of the following is the correct definition of the limit? The lim f(x) = A, if and only if, for…

A: Explanation of the answer is as follows

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Q: S 4x* sin2x dx A (2xª + 6x² + 3) cos 2x + (4x³ + 6x) sin 2x + C C (2xª – 6x² • 3) cos 2x + (4x³ –…

A: Integrating by parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx dxndx=nxn-1 ∫cos(ax)dx =1asin(ax)+C ∫sin(ax)dx…

Q: Find the area of the region under the graph of f(x) = 2x² – 4x + 2 on [-2, 3].

A: Given query is to find the area under the curve.

Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

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Q: Consider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

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Q: a²f If f(x, y) = xey + 8xy, then , is given by: O + 8 O 4xe4y + 8 ○ 웃+8 O 4e4y + 8 O None of these…

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Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 4x + 4. (Use…

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Q: The design department of a shipping company is constructing a box in the form of a rectangular…

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Q: The volume V of a nght circular cylinder of radius r and height h is V= 7rh. (a) How is related to…

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Q: dy 6-x.-3y= x' dx

A: we are given an ode -x*dy/dx -3y=x2 we have to solve this ode as we can see, this is a linear first…

Q: Find the total area of the region between the x-axis and the graph of y = - x´ - 3x, - 4 <x54.

A: Given query is to find the attached area of the region.

Q: 23. (x- 1) (x + 1)

A: Given: x2(x-1)2(x+1)

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of  PQ.…

A: Given problem:- Find the directional derivative of the function at P in the direction of PQ. f(x, y)…

Q: 2+ y =x+ - 2x3 1 y = 0 2 -1

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Q: Find the maxima and/or minima of f (x, y,z) = 2x2 + y2 + 3z2 subject to the constraint 2x - 3y - 4z…

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Q: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: dy + y = y² sin x dx

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Q: 2. Let a, b e R and let f be the function Z + Z defined by f(z) - ar + b. For which values of a and…

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Q: 2. Find the limiting values of 3x? + 5x - 4 (i) 5x? - x +7 as x→ 00

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Q: Given the following function. - if x2 x > 2 x-2 5, if x = 0 or x = 2 Can f continuous at (-1, ∞)?…

A: Here, for the given function: limx→0-f(x)=limx→01x1+x-1x  (∞-∞…

Q: r = 2sin30 * %3D circle rose inner loop cardioid dimpled convex spiral lemniscate

A: Given problem:- r=2 sin(3θ) To find :-  shape of graph of given polar equation

Q: -2 -2 3 -9 9. A = -3 -5 8 2 -2 -2 -3 Find a matrix P such that D = P-'AP is the Jordan canonical…

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Q: a) Find the points of intersection of the curves y = -x? and y = x? – 2. b) Find the Volume of the…

A: answer is in next step

Q: A hot air balloon sing vertically is tracked by an observer located 3 miles from the lift-off point.…

A: let the height at that moment is h miles.

Q: Assume a, b and c are real numbers greater than 1. Find p, q and r so that the following equality…

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Q: Use Euler's Formula to express each of the following in a + bi form. Use symbolic notation and…

A: i) -e3π4iii) eπiiii) 5ie-π3i

Q: f(-9) = 0 f(-1) = 0 f(2) = 2 f(4) = 4 f(6) = 3 lim f(x) =∞ lim f(x) =-∞ X--5+ lim f(x) = ∞ lim f(x)…

A: Concave up:(-∞, -5) : f''(x)&gt;0function is decreasing in (-∞, -9)f'(-9)=0and function is…

Q: f a company's cost function for a product is C(q) = 2290 + 3.8q + 0.004q2 %3D and the revenue…

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Q: The shape of the Gateway Arch in St. Louis is approximately a parabola with a base and a height…

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Q: dy +y=e' xp

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Q: 2. When buying a new car, one consideration is how fast the car loses value, known as the…

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Q: 3. Solve r"(t) = subject to the initial conditions: r(0) = and r'(0) =

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Q: Given the points A(-1, 2, 0), B(1, 0, 3) and C(1, 0, 2), find AB • AC x BC.

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Q: | cos(Vx) dx A 2 Vx sin (Vx) - 2 cos ( Vx) + C C 2 Vx sin x (Vx) - 2 cos (Vx) + C B 2 Vx sin (Vx) +…

A: To evaluate: I=∫cos xdx Substitute x=u⇒12xdx=du⇒dx=2udu So, I=∫cos u 2u du=2∫u cos u du

Q: Set up and evaluate the triple integral in spherical coordinates needed to compute the volume of the…

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Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x2 from x = 5 to x…

A: Explained below

Q: Given the cost function for a product: C(q) = -0.00932q + 0.196q? + 1.43q + 36, at what level of…

A: Find your answer below

Q: Solve the right triangle. Round your answers to the nearest tenth. A = b-0 56° 22

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Q: sin(x) dx Jo

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Q: Which of the following gives the formula for the inverse of the function x + 3 f : R \ {-7/2} → R \…

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