Show diagram, define variables, state formula, theorem, equation or function used, Show substitutions and or steps in solving an equation, State restrictions, state concluding statement, Use correct notation.

Q: 2. Find the area of the rectamgle with base on the x-axis and two of the vertices on the graph of…

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Q: Let y = f(x), where f(x) = x + dy = 33. X Find the differential of the function. X

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Q: Evaluate. 5 Ĵ - 3 (4x² - 5x+7) dx

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Q: (a) [ƒ(x) + 9(x)]| d dx d (b) f(g(x))] dx d dx (c) · |[(x)6 · (x)ƒ]² x=1 d [g(x) (0) dx f(x) x=1…

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Q: fe-In x³ cosh (2 ln x) dx

A: The given integral  is

Q: 1. Determine whether the statement is true or false. If it is true, explain why. If it is false,…

A: Fermat's Theorem: If f(x) has local maximum or minimum at x=c and f'(x) exists at x=c then…

Q: Evaluate the definite integrals. (a) f (b) √2x + 1dx ²/4 S cos (√) √T dx

A: Evaluate the definite integral

Q: Evaluate the Based [ -√4-42 -JT-y² integral Using CYR coordinates the figure given. Show work & some…

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Q: Question 6. (b) problem, Describe in general terms what it means for an ODE to be stiff. Recall that…

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Q: please do the other one

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 5 in.…

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Q: If y = (x8 + 9), find y' (1). O 10 In (10) - 8 O In (10) - In(10) + 4 O 10 In (10) + 8 08

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Q: f(x) = sin(x), a = π/6, n = 4, 0 ≤x≤ π/3 (a) Approximate f by a Taylor polynomial with degree n at…

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Q: Solve the given differential equation by using appropriate substitution. The DE is homogeneous. -y…

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Q: 7. Evaluate DETAILS LARCALC11 15.7.504.XP. curl F.N N dS where S is the closed surface bounded by…

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Q: Suppose that the perimeter of a particular Norman window is o be 40 ft. What should its dimensions…

A: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

Q: Truck Rental Company Y rents out a moving truck for one day by charging $25 plus $0.07 per mile.…

A: If the rate per unit is  then the rate per units is .

Q: Given the vector u = 67-37, find the magnitude and angle in which the vector points (measured…

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Q: I The curvey = tan x crosses the line y = 10x at a non-zero x-value between x = 0 and x = . Use…

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Q: Calculate[ri(t) · r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly and…

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Q: An investment appreciates 2% per year. Originally $5000 is invested. What is an equation to model…

A: An investment appreciates 2% per year. Originally $5000 is invested what is an equation to modal…

Q: Volume of the Solid Beneath -* and above the region Find the the cylinder f(x,y) = e r = {(x,x): 0 ≤…

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Q: he masses m, are located at the points P,. Find the moments Mx and M, and the center of mass of the…

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Q: Radioactive Decay Phosphorus-32 (P-32) has a half-life of 14.2 days. If 500 g of this substance are…

A: Given:Half-life of Phosphorus is 14.2 daysThe initial substance was 500 gmFormula Used:Initial…

Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ² ||ti + 1²j||dt

A: To evaluate the following integral.

Q: A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after…

A: The equation of online sales is

Q: You want to build a 1200 square foot rectangular infinity pool. Three of the sides will have regular…

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Q: y-values O₂ 8. 7 6 2 1 If f(x) g(x) h(x) -, then g(x) x-values Submit Question ƒ'(1) = Question…

A: The quotient rule of derivative is

Q: Use the graph of the given function to answer the questions below. -4 -3 -2 -1 y 24 lf 1 2 3 X

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Q: A motorboat take 3 take to travel 144 kilometers going upstream. The return trip takes 2 hours going…

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Q: Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values…

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Q: Set up the triple integral of an arbitrary continuous function f(x, y, z) in spherical coordinates…

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Q: Create an equation to which the following solution apply: y=e^(-6x) and y=e^(-x) In the form of: y"+…

A: Solution is given below in details.

Q: Find the area of the shaded region. square units 2 1 -1 y=x² - 2x³ y=0 2

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Q: Oil leaks out of a tanker at a rate of r = f(t) liters per minute, where t is in minutes. If f(t) =…

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Q: At a seaport, the depth of the water during the day can be found using the equation (-8) = 6.0 COS…

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Q: Consider the surface x = 5y² + z² - 177.

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Q: 3. Find the area under the curve y = xe-² from x = 0 to x = 2.

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Q: •/F. Evaluate F. dr. F(x, y) = xi + yj C:r(t) = (9t + 1)i + tj, 0sts1

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Q: If f(x) = 12x² – x³, what is the rate of change of f'(x) at (1, 11)? -

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Q: Evaluate the definite integral. L₁ (2² - 2)² dx X 9.73

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Q: 5) Find the length of the polar 3π curve r(0) = -2 cos 0 where 0 runs from to 2

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Q: (c) (d) Use trigonometric identities to show that sin (3x) = 3sin(x) - 4sin³ (x) Use trigonometric…

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Q: 2 [² x²√1+x³ dx 2 0 1 2x 1+x² dx xxt: TTS Jo 2 So 0 x ecos sin x dx x²v1+x dx 2x 1+x² dx

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Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

A: Given :find the local maximum and minimum values and saddle points of the function.

Q: Use the Chain Rule to find and 3 where z = (y-x), z = s²t, y = st².

A: The solution is shown in step-2

Q: 8-. Show y = ³ + 3x + 2 satisfies the differential equation y" + xy" - 2y = 0.

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Q: 5. Graph the polar equations. If you use a table, show your work: a. r = 3 sin 0

A: As per the new guidelines we can solve only one r = 3 - sin(θ)

Q: A favorite aunt wishes to establish a trust fund for her niece's math education. How much should she…

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Q: A new series of tests is carried out and the equation modified to  y"+2y+5=0 y`(0)=0 y=20 t=0…

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