Convert the following polar equations into Cartesian equations: a. r cos(0) = 2 b. r= 4 sec (0) c. r = cot(0) sec(0) d. r sin(0) = r cos(0)

Q: (a) For what values of r does the function y = ex satisfy the differential equation 7y" + 34y' - 5y…

A: We use the techniques of higher order differential equations to solve the given problem.

Q: Use the formula K(t) k(t): ||r'(t) x r" (t)|| ||r' (t) ||³ r(t) = 7 cos(4t)i + 7 sin(4t)j + 5tk = =…

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Q: Calculate the moment of inertia of the shaded area about the x-axis. 96 mm Answer: Ix = 96 mm 57 mm…

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Q: If the total cost function for a product is C(x) = 200(0.02x + 3)³ dollars, where x represents the…

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Q: Р Find the directional derivative of the function fo the vector (3,-3).

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Q: = √ 1 /1₁ ₁ x² dx = Given that 2 6²16-9 (6 - 9x²) dx. use this fact and the properties of definite…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let f and g be differentiable. Using the given information, compute for K'(2) when K(x)=f(x)g(x).

A: given K(x)=f(x)g(x) To find : K'(2)

Q: Explain why lim (2x-3) = 3 with an ε = 0.01 is not a limit.

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Q: Find f(x)g'(x) dx, given that ff'(x)g(x) dx 1.3 and the values in the table: xƒ(x) ƒ'(x) g(x) g'(x)…

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Q: A college student works for 8 hours without a break, assembling mechanical components. The…

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Q: 1. กำหนดให้ y = un - น และ u = x-x จงหา dx (Ans, 4x - 6x + 4x −1)

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Q: If f(x) = 7+ Find f'(x). Find f'(x). 10/8 + 4 x²

A: Given that a function f (x) = 7+ 5/x + 4/x2.  And we find f'(x) and f"(x).

Q: (1) (5,4) (Ans. 5√3 5 22

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Q: If f(x) ƒ'(x) = ƒ' (2) = = 3 sin x 3 + cos x then

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Q: A vacationer on an island 8 miles offshore from a point that is 48 miles from town must travel to…

A: Given,a vacationer on an island 8 miles offshore from a point that is 48 miles from town must travel…

Q: Suppose a population grows according to a logistic model with initial population 1000 and carrying…

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Q: Evaluate the definite integral. lo' (e1¹341 + 13 0 ¹i+e¹¹j + tk dt

A: The solution is shown in step-2

Q: Find €13 (3) by Parametric Functions method √t { y = 1 - / ที่ 1 = 4 (Ans. 1

A: The solution is shown in step-2

Q: Determine whether the series n=11+2+3+..·+n is convergent or divergent.

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Q: State the domain and range of the function f(x) = 13+ log7(x) Answer: domain= range = ↳ ✓

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Q: Esc 85°F Mostly sunny F1 x−3 7-9 O the limit exists for any c O does not exist when F2 C = -3 O C =…

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Q: [2-2x] = 2 with an & = .01, 6= O this is not the limit O -0.02 O 0.02 O 0.005

A: Let means that for every >0, there exists a >0, for that for every real x,  when ever,

Q: Use the parallelogram method to find the following sum v + w when v = (-5, 4) and w= =(5, 4). (0,0)…

A: We have to find the following sum v + w, when v = (-5,4) and w = (5,4) by using the parallelogram…

Q: 6 Let (u, v) be the inner product on R² generated by A = - [ -1 and let u = (3, −5), v = (7,4). Find…

A: We have to find the .

Q: = A lune occupies the region inside the circle x² + y² = 8y but outside the circle x² + y² Assume…

A: y=

Q: Suppose that the power series Cn (x-2)" converges when a = 4 and diverges when x = 8. n=0 In each of…

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Q: Find a formula for the nth term of the arithmetic sequence. a1 = −4,  a5 = 8

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Q: 2. f(x) = 3x²-3x+1 2x (Ans. 31 2 21

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Q: Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then…

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

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Q: 4. Sds, C is the line segment from (1, 4, 1) to (3, 6, 3)

A: Given that  ,C is the line segment from (1,4,1) to (3,6,3)

Q: 6-For the y= 3x v4-x², determine the absolute max and min values within its domain.

A: The given function is

Q: Find a formula for Ry and compute the area under the graph of f(x) = 24x² - 4 over [2, 5] as a…

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Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

A: Given that ,The fence on the side opposite the river costs = $40 per footThe fence on the other…

Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e9, where the value ab is as…

A: Here we want to find the minimum values of the product  subject to the constraints..Let's consider…

Q: Q72 There is a minecart in a mine that is 5900 kg. The minecart reaches the end of the track and…

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Q: mx2+x² does not exist for every c X- O True False

A: The given limit is

Q: Let f and g be differentiable. Using the given information, compute for J'(0) when J(x)=f(x)/g(x).

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Q: Use sigma notation to write the following left Riemann sum. Then, evaluate the left Riemann sum…

A: The given function is on  with  The left Riemann sum of the function f(x) over a given interval…

Q: A store's sales on day x are given by the function S(x) below. Find the average sales during the…

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Q: Let z(x, y) = -5e* sin(y) where x = t & y = 2nt. dz dx dy dt dt dt Calculate da dt dy dt = 978 = 2π…

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Q: If ƒ(x) = 2x sin x cos x, find ƒ'(x)= Find f'(4) =

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Q: Find 1₁ -2x + y da, where R is the parallelogram enclosed by the lines 2x+6y R -2x+y=0,- 2x + y = 4,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the parametric equation of the line passing through the points P = (1, 2, −1) and Q = (1, −1,…

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Q: 5-As a snowball melts, it's volume decreases. The volume in cubic centimeters is given by the…

A: Let the volume of snow ball=V Let the radius of snow ball=r cm

Q: •π π sin y 0 X y dydx

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Q: 3- Find the derivative of (sinx +x)/(2+cos x).

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Q: Choose a polar equation that is symmetric about the polar axis. Or= sin²0+4sine Or= sin²0+4 cose O r…

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Q: The owner of an orange grove must decide when to pick one variety of oranges. She can sell them for…

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Q: 2) Find the domain and range for the following functions: a) y = ²²-² b) y=√x-3x² c) y= 3+2 cos x…

A: Domain :- It is the possible values of x where the function is defined.Range :- It is the values of…