DO NOT include spaces in between characters. And, DO NOT include dy/dx in your answer. dy Determine given x = sin (x+ y). dx

Q: Problem 1: Evaluate the following definite integrals. Sx(x2 + 1)V4- 2x2 – x dx -dx

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Q: PART II. Find the derivatives of the following expression, solution must be presented. 1. x²y – ỹ =…

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Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 => (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: A. Evaluate the limit of a function using the concept of Special Limits. 1. lim t→0 t t2-3t+5 + t2-1…

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Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

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Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

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Q: Find the AuRtaYe value of f(x) = x* on the intervai 2,67

A: answer is in next step

Q: 1 Calculate the difference quotient for f(x) = at a = 4. V2x + 7 (Express numbers in exact form. Use…

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Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Here we have to solve the given differential equation x2dy+3xy-1dy=0 ............................…

Q: 1. Solve letter a and letter b. Show t complete solution. а. Find of the dy dx function 9x* + tany…

A: Topic:- derivatives

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x² + 16

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = for f(x) = cos(x). %3D T2(x) must…

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Q: Note Answer One Question Q1 The following data is provided for the velocity of an object as a…

A: Let's find.

Q: Check the continuity of the function f(x). Explain why f(x) is continuous or not. x+1 =,x x2X > 1

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Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: The water is leaking at the rate of π/2 m³/min.

Q: Q4) Find plane area inside the polar function r = 2sin E- 0) and outside r= sin -0) in first…

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Q: Using trigonometric substitution, given (Vx+64 dx, the simplified form of the integral is: sec³ed®…

A: We have to check whether the given statement is true or false.

Q: Question 2 Evaluate: J y* sech (e m)tanh (e ), 7Iny @ -ch(v^) +C B) None -ech-(7) +C 7 ® ech (»*) +c

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Q: Evaluate the following integral using Trigonometric Substitutions Method: п 2. y = 1- x dx

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Q: Consider the integral 5 x (z° +1) dx. In the following, we will evaluate the integral using two…

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Q: Evaluate +V7dx 3 Oa.5 +C 2 5 3. Ob.2 3 2 Oc 2 sm +- Ot ast Od +C 3 2 52~

A: Evaluate integral

Q: Find the distance between the skew lines: x = 4+ 9t, x = 4 – t, y = 3+ 2t, z = 7 – 4t y = 9, z = 8+…

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Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: Find volume of body bounded by z 0 from below and z = 4 - y from above inside y = x2 ,y = 4 .

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Q: 2 dr sech 2r= e2r +e-2r A) True B) False

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Q: The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial…

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Q: To find the distance across a river, a surveyor choose points A and B, which are 232 m apart on one…

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Q: Consider a function () whose dertvative ') continuous as shawn below Graph of f'(x), NOT f(x) 1 5 -1…

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Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: Given Ax) = - 2 use the first principles definition to find f'(1).

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A: Set up the triple integral and solve to get the desired volume.

Q: is satisfied. Finally, to determine if Rolle's Theorem can be applied, we also need to check if the…

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: O Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2, y =

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Q: applying substitution méthöd: sqns -48

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Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

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Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: Let's find.

Q: 3 5 8x 15 dx 5 x4 |

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Q: Solve the following differential equation by the method of Variation of Parameters: x" + 49x csc…

A: The given differential equation is;  x''+49x=csc2(7t).

Q: Q2) Convert the polar functionr= tan20 to cartesian.

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Q: The limit represents a derivative f' (a). Determine f(x) and a. 14h lim 1 h→0 (Express numbers in…

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Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

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Q: (4x* – r*y +y*)dx + x*dy = 0.

A: Let's find.

Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

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