1.1 Exercises In Problems 1 Q-120, a differential equation is given along with the field or problem area in which it arises. Classify each as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear. dy 3. dx y (2 – 3æ) а (1 — Зу) - (competition between two species, ecology)

Q: Find the slope of the line tangent to the conic section 25 (x+3), (y+2)² = 1 at (3,8). 36

A: We find the slope of tangent to the given conic with the help of calculus .

Q: 11 7

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Q: 3. Graph the polar equation and find the area of the region. Outside r = 1 but inside r = 2 sin 20

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Q: 1 - x dx. e + x Evaluate:

A: We have to find the given integral.

Q: Estimate f(x) = 2x2 the area under the graph of the function from x = 2 to x= 19 by a Riemann sum…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

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Q: Evaluate the following double integral and enter the value into Ans: || 7xye"vdA, R = [0,1] × [0, 3]…

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Q: inal the @ e w and cone an ave cof the Cuarve?

A: here i am providing my hand written solution

Q: 1 g(x, y) = cos (Tx VT) + log3(x – y)' Calculate the instantaneous rate of change of g at the point…

A: To solve the following problem

Q: If cos e = and tan e < 0, 25 what is the value of csce? 25 24 A B 24 25 24 25 C D 25 24

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Q: Calculate the left rectangle approximation of 3x- dx using five subintervals.

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Q: Find the series' radius of convergence E (3x)n n=0 O1 00 O 3

A: This question is related to infinite series, we will solve it using given information.

Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: The given function is  h(x,y)=x3-3x+3xy2

Q: Q/ Evaluate the integrals :- 1 + Z

A: This question is based on indefinite integral.

Q: 1 - 5e -jwt dt + 5e -jwt dt -1

A: integration

Q: 4. -1 y%3D 3x-9

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Q: 12. r + 2y? + 20 = 0 (A) not a function (C) function; domain: (0, 00) (B) function; domain: R (D)…

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Q: S 2æe3= dx ,3z 9.

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Q: Evaluate this double integral. Avoid integration by parts. Hint: Can you reverse the order of…

A: Let's find.

Q: If a = (-6, 12, -9), b = (2, -16, 18), and c = (28, -14, 3), what is %3D %3D (51, 0, -24) (57, -48,…

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Q: Lagrange Multipliers will be used in order to solve the following: Maximize f(x, y, z) = 4.x + 2y +…

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Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

A: Given problem:-

Q: Given the triangle 17 find the length of side x using the Law of Sines. Round your final answer /37°…

A: The triangle has length 17, x and angles 37°, 14°

Q: nP 00 クの In=1 2+n3

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Q: Use the price-demand equation below to find the values of p for which demand is elastic and the…

A: We have to use the price - demand equation to find the values of p for which demand is elastic and…

Q: Use the figure to derive the formulas for sin), cos(), and tan cos e 0 sin 0

A: A right triangle ABC is formed inside a circle:sides are: (1+cos θ), sin θusing Pythagoras…

Q: 4) What is x to the power of -6?

A: The exponent of any number represents how many times to use the number in a…

Q: First question: Find the inverse and determinate of the matrix A = [??H] -1-3 1 3 60 1 0 1 ||

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Q: 2 is a critical number of the function f(x) = /2x – x². Select one: OTrue O False

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Q: Solve a3 -4x2 +4x lima→234 –12.a³ +12a²

A: We have to solve the given limit.  We can use Factorisation method.

Q: Show complete solution. Please make sure that your handwritten is readable. Thank you

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Q: The dimension of the vector space P3 is equal to: Select one: O 5 none of the others O 2 4 O 3 ):…

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Q: 2 [arc cos ( Incs-2) fdz ( Incs-z>) ] dz

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Q: For the function: f(x) = 2sin (G) on the interval [0,4Tt], find: Relative max = (t,[ ? ]) Relative…

A: This is a problem related to maximum and minimum of the function. Based on the general formula and…

Q: EXERCISE 2 Consider f(x, y) = 3x² – 4y² and = = cos T î + sin 7 ĵ. Use the Theorem above to find the…

A: This is a problem related to vector calculus. Based on the general formula and concept we will…

Q: 31) Find a company's total-cost function if its marginal cost function is C'(x)=5x2-7x+4 and C(6)=…

A: Marginal cost function of a company is given is , C'(x) = 5x2 - 7x + 4  Also C(6) = 260 We have to…

Q: Julissa wants to find the measure of ZA in A ABC. Step 1: 11 = 7? + 9 - 2·9.7.co COS X Step 2: 121 =…

A: A detailed solution is given below

Q: Solve a3 -4x2 +4x 3x4 –12x3 +12x2 limp→2'

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Q: (a) lim g (t) (b) lim g (t) t 2 t-3

A: answer is in next step

Q: 3 6. Work Problem 3 (e ): v1 = 0 |, U2 = 02 vectors from %3D 1 a) [' Determine if the vectors {v1,…

A: Vector

Q: A bowl of soup at 95 C (too hot) is placed in a 22•C room. One minute later, the soup has cooled to…

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Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: Evaluate fE in two ways: using partial fractions and using a trigonometric substitution." Reconcile…

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Q: 7x +4 1+1 if I1 1. Evaluate f(-3) (A) –17 (C) 11 (B) 10 (D) undefined 2. Evaluate f – 2() (A) –10…

A: Topic:- function

Q: Evaluate the following integrals. Show all the necessary solutions. 3. tane de ) 71+ In cose)43

A: Given problem:-

Q: 3. Given z (1- i2), find z-1 4. Let w = f(z) = 2iz + 67, find u and v and the value of fat z =+41…

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Q: Find the area under the graph of the function over the interval given. 32) y =x2 +1; [0, 1] A) D)를…

A: Given :y=x2+1   0,1

Q: The intensity levels I of two earthquakes measured on a seismograph can be compared by the formula…

A: Just use input given and calculate I1/I2

Q: ) What number is next in the equence? 2, 4, 16...

A: What number is next in the sequence? 2, 4, 16 ...

Q: Calculate the test-statistic, t with the following information. ni 20, ãi 2.37, s1 0.3 %3D n2 = 30,…

A: We have to find the test statistics.