Graph the following function and find the area under the curve on the given interval. f(x) = (144-x²)-², [0,6] -2

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Q: (a) y" + y = cos(x); y(0) = 1, y'(0) = -1.

A: Given

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Q: ntegral Calculus - Plane Area 1. Find the area in the first quadrant enclosed by y = (x2 + 4)/x2, x…

A: Topic = Area

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A: xy2dy=(y3-x3)dx  y(1)=2

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Q: 2. Suppose that f(1) = 2, f(4) = 7, f '(1) = 5, f '(4) = 3, and f" is continuous. Find the value of…

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Q: Find the first derivative f' and the original function f. f"(x) = x³ - 12x, ƒ'(1) = 0, ƒ(1) = 10

A: Topic - Differential equations We are given f''(x)=x3-12x ,f'(1)=0 ,f(1)=10 ∫xndx=xn+1n+1+C

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Q: how did the operation change right after you equated dA/dL to 0

A: For finding maximum or minimum , firstly find critical point . For critical point , equate first…

Q: Determine if the sequence is monotoric and if it is bounded. fo 7. an = (n+7) ! (n+1)!

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A: Solve the given

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 2 - 1² st F(x) = F'(x) =…

A: Please see the below picture for detailed solution.

Q: Solve the differential equation. dp dt = t²p 3p + t² - 3

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Q: Use implicit differentiation to find da/dt if a - t4 = 6a²t. - Answer:

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Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

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Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x a = b =

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Q: 3. Use the Ratio Test to determine the convergence or divergence of the series. 00 n! a. En=0 3"

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Q: 32. √ ₁²+2x-3d²

A: Given integral I=∫xx2+2x-3 dx

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: the answer -25 is incorrect. Is there something wrong with the way the problem was done? I do not…

A: Let's find dz/du by using chain rule.

Q: Suppose that the cost, in dollars, for a company to produce a pairs of a new line of jeans is…

A: Suppose that the cost, in dollars, for a company to produce x pairs of a new lines of jeans is…

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A: Given query is to find series converges or diverges.

Q: You go to the doctor and he gives you 16 milligrams of radioactive dye. After 12 minutes, 5.75…

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Q: I want to know why the absolute minumum value is -6.35.

A: Let's solve for absolute minimum value.

Q: 4. Use the Root Test to determine the converge or divergence of the series. " b. 21(3n+1)" a Σ=1…

A: The given series, a) ∑n=1∞n2n+1n b) ∑n=1∞2n+1n-1n c) ∑n=1∞n3n We have to test the convergence of…

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Q: 20 20 8.) For the tangent line to f(x)=e* at x = 0 to have an error of at most 0.1 in approximating…

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Q: Domain and hange. Find the domain and range of the function. 5x² + 4 for 0 4 x 42 L

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Q: (D² -3D +2)y= (1+ex)-¹

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Q: x+y+z = -3 -7 2x - 2y-z = −7 -3x + y + 5z = 5

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Q: Given that f(x) = 2x+cos(x) is one-to-one, use the formula to find (f ¹)'(1). (f ¹)'(1) = 1…

A: Given that :  f(x) =2x + cos(x)  is one to one    To find : (f-1)1 using the formula (f-1)'(x)…

Q: 3. Find the degree measure of the angle given in radians, and draw the angle in standard position.…

A: Here we have to find the degree measure of angle given in radians.

Q: Identify the correct equation for the given graph below: y = 12x³(x-2) Oy = 12(x-2)²(x)² Oy =…

A: Given query is to find the equation of the function.

Q: Estimate the area under the graph of f(x): approximating rectangles and right endpoints. Rn = = L₁ =…

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Q: The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge…

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Q: The volume of a cylinder of height 10 inches and radius 7 inches is given by the formula V = 10mr².…

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: An equation for a quartic function with zeros 4, 5, and 6 that passes through the point (7, 18) is…

A: An equation of a quartic function with zeros 4,5,6 and passes through (7,18) is