Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. π/2 2 cos4 x dx, n = 4 M4=

Q: A student is asked to determine the polar coordinates (r, 8) corresponding to the Cartesian…

A: Let's find.

Q: A 16 cm x 10 cm open rectangular box is to be constructed by cutting square corners out of a piece…

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Q: Find dy/dx: solution in handwritten 1. y = , Vu du

A: Note:- Here limit of integral 0 to t4  then in your question we need to find dy/dt instead of dy/dx…

Q: n 2 (4k – 2) = k=1

A: Recall:  1+2+3+...+n=n(n+1)2

Q: Find the minimum value of f (x,y,z) = 2x² + y² + 3z² subject to the constraint 2x - 3y - 4z = 49

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Q: The amount of garbe, G produced by a city with population p is given by G = per week, andp is…

A: As per our guidelines, we can help you in solving only first problem, rest of the problems you have…

Q: Find the general solution of the given differential equation. x + 2y = x³ -x dx y(x) = Give the…

A: Here, the given DE is: xdydx+2y=x3-x⇒dydx+2yx=x2-1 Comparing it to dydx+yP(x)=Q(x). We have P(x)=2x…

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

A: r1=9ti+3t2j+8t3kr2=t4k

Q: By total differentiation, determine or find the approx. change in the length of the hypotenuse of a…

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Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.

Q: If A =27+7-, B =-T+27-4k, and A +B +C =27+7+ 2k, what is C? 7.

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Q: 1 x + ex 2 g dx

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Q: where t € [0, 1]. x = cost, y = sint-t,

A: Here we will find the equation of tangent and length of curve P,

Q: y² − 5y = x³ - e² +c where c is the of integration. Setting x= we have . Thus, we have y — 5y — ( —…

A: This is a problem related to integration. Based on the general formula we will answer the question.

Q: 1 et f(x) = = . X Find the tangent line to the graph of the function at x = −1. y = 【 Find the…

A: Follow next step

Q: 2. Find the area of the region bounded by the curve r = 2 cos 30 .

A: Given problem:- Find the area of the region bounded by the curve r = 2cos(3θ)

Q: In order to solve with we first write and Setting to get sin 2xdx + cos 3ydy = 0 y(π/2) = π/3 cos…

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Q: Find the arc length L of the graph of r(t). r(t) = 1³ i + 1 j + = √61² k, 3≤1≤7

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Q: Given the equation r In(y) = z Arctan(3*y). Assuming z as a function of variable dz and y, find

A: The given equation is xln(y)=ztan-13zy ........................................ (1)  Here z =…

Q: Given the general solution for a system X' = AX, X=C 2 + C2 e and 2 find the value of Ci & C2. 4 the…

A: Given;  X'=AX X(0)=(2            4).

Q: 5. Evaluate sin y - dy dx y

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Q: Use Chain Rule to find ds given w = Vr² – 2y + z² and r = cos (st), y = -2s Int and z = s –

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Q: parallelogram is formed in R3 by the vectors PA = (3, 2, -3) and PB = (4, 1, 5). The point P = (0,…

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Q: Let f(x,y) = 4(x + 1)²(y - 1) - y² - 8x²-16x + 2y - 18 (i) Find the sum of all x- coordinates of the…

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Q: analyze and trace the given curves y = x2 + 1 / x2

A: Explained below

Q: 7) Find the unit tangent vector T(t) for the curve given by r(t) = 2 sintỉ+ 2 costj + tantk when t =…

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Q: Find the Taylor series generated by fat x = a. 1 f(x)=, a=9

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Q: Evaluate the limit lim f(t) where f(t) 7' + 19'\ for t 0. 2 lim f(t) =

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Q: Problem 3. Solve 2+2 =10 4* +4 = 68

A: To solve the following system of equations.2x+2y=104x+4y=68

Q: Select the conic section represented by the equation. 13x 2 + 5y 2 - 6x + 3y - 5 = 0 circle point…

A: We can select the conic section as below.

Q: Determine whether the series converges or diverges. 4n³ n²-4 n=2

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Q: 1 lim (x² –1)sin x+1

A: To find out the limit.

Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

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Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

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Q: Solve the system using Cramer's Rule. - 6z + 2y + 6z = – 14 - 3z - 4y + 5z = – 6 - 5z + 3y –2z = 1…

A: To solve the following system of equations bu using Cramer's…

Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

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Q: 7. f(x) = x* - 4x³ +3x? +4x – 5 Domain: y Range: Rel. Maximum(s):. Rel. Minimum(s): End Behavior: As…

A: We have to find the graph, Domain, Range, relative maximum, relative minimum, End behaviour,…

Q: Find all partial derivatives of w = x sin(yz) – z In(xy)

A: To find all the partial derivative.

Q: The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x² - y² + 2z +…

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Q: Find the equation of the tangent line to the function y = xsin x when x = 6.

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Q: Find the period of y=-3cos(3.7x). Round your answer to 1 decimal place.

A: " Since you have asked multiple question we will solve first one for you. Please specify question…

Q: Solve the system. Give your answer as (a, y, z) 3z - y + z = 7 -2x + 2y + 3z = – 18 3z-6y + 6z = 0…

A: Use the method of elimination and find the value of x, y and z.

Q: 5. Does the function f(x) = e2x - 2x have any points of inflection? Justify your answer.

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1 = lim t+x6t²+7'2t (?, ?)

A: Explanation of the answer is as follows

Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

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Q: g expressions a. lim (2z - 1)(2-1)

A: Given : apply chain rule    find limit of about separately

Q: Solve the given differential equation by undetermined coefficients. y'' + y = 6x sin(x)   y(x)=

A: Follow step 2nd .

Q: Let C be the parametric curve defined by x(t) = t² – t – 2, %3D |y(t) = t3 . 1 t² +t. 2 - (-2) 3…

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Q: Question 7  A business spends $80,000 on Marketing, $100,000 on R&D,  and $ 12,000 on Expenses.…

A: We have to find the ratio between spending.

Q: 5x-10 Find the area under the curve of f(x)=- 05 O-10In 2 O 5-10lm 2 0-5 from 1 to 2.

A: Solve the given