For what value of the constant c is the function f continuous on (- o0, 0) where S (1)² – c if y< 2 f(y) c(y) +1 if y > 2

Q: Use cylindrical coordinates to calculate the triple integral w S(x, y, z) dV for the function f(x,…

A: To evaluate: ∫∫∫wf(x,y,z)dV=∫∫∫1784zx2+y2dV Here, the region of integration is x2+y2≤z≤28-x2+y2…

Q: 1. cot? 2x csc* 2x dx

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Q: 11 2

A: We can solve this as follows:

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: Solve the DE: tan xsin y y'+(3 tan x-2 cos y) sec x=0

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Q: Determine whether u and v are orthogonal, parallel, or neither. u = -9i + 80j - k v = 9i + j - k O…

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Q: A cone was formed by rolling a thin sheet of metalin the form of a sector of a circle 72 cm in…

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: Fove that y = ln|| is a solution to 1+e-22 - xey-x² . Use the initial values x = 0 and y = 0.

A: Given query is to find the solution of the differential equation.

Q: A ball is thrown vertically upward. Its height h feet after t seconds is given by the formula…

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Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: 1 EVA LUATE ECs) OF THE DIFF ARD 4(0)-0. dy dt² dt

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Q: EVAUATE FL) OF TRE DIFF ERENTIAL EQUATION AT zEto NITI AL CONDITONE. oit

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

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Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Which of the following trigonometric expressions is NOT equivalent to 1? * csc? 0 – cot² 0 cos? 0 +…

A: To determine which of the given trigonometric expressions are not equal to one.

Q: Using any methods discussed, find atleast 1 root for each problem. Upload your solution at the space…

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Q: 1+cos4x 1. 1-cos4x -csc2xdx

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Q: Evaluate by using homogeneous D.E. 3 (3x? + y) dx – 2xydy = 0 03 In(x2 + y?) + 4 = C O a = C(9x³ +…

A: To evaluate by using homogeneous D.E.33x2+y2 dx-2xy dy=0

Q: Evaluate the following IMPROPER INTEGRALS. It is optional to double check your answers/solution for…

A: To evaluate the given integral.

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The length and breadth of the floor of a room are 30 feet and 20 feet, respectively. Square tiles of…

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Q: 2. The growth rate (in inches per year) of the diameter at breast height of a certain tree is given…

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Q: A mass that weighs 8 lb stretches a spring 48 in. The system is acted on by an external force of 8…

A: Given

Q: Calculate L4 for f(x) = 24 cos () %3D L4

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Q: integral. Give your answers as fractions 3 (i) dx V1- x2

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Q: Find the slope of the line passing through the points (-1, 3) and (-8, 3). slope: | Find the slope…

A: Solution ) slope  m = (y2 - y1)/( x2 - x1) 1) point ( -1 , 3 ) , ( -8 , 3 ) slope m = ( 3 - 3 )/( -…

Q: A hollow cylindrical metallic pipe is open at both ends and its external diameter is 12 cm. If the…

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Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: The shaded region shown below is bounded by the functions f(x) = -3x2 + 8 and g(x) = 0.5x + 6 and…

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Q: (x² + y² ) dx – xydy = 0 O 2y = x In cx² O y? = x² In cx²

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Q: 345 cos dx 1-cos24x+sin? 4x

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Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

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Q: What is tan 0 if sin 0 = cos 0? -1 1 O Option 1 O Option 2 4 O Option 3 O Option 4

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Q: Determine whether P = and Q = are orthogonal vectors. If W = and V =, compute V x W. If W = and V =,…

A: Explanation of the answer is as follows

Q: S x³et*dx

A: A detailed solution is given below

Q: Let à =, B = and Č = a) (à · B)č b) Ả · (2C) Find C)

A: A→=1,-2,3, B→=0,2,4, C→=5,-1,-3a)…

Q: 11x +625 The average cost for a company to produce x units of a product is given by the function…

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Q: 5. Given the equation: (x + 2y – 4)dx + (2x – 4y)dy Solve the differential equation. Choose your…

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Q: Consider the function y = 3x2+2x-4. What is the exact value of C in the interval [-2, 4] such that…

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Q: Evaluate using Linear Equations. v(dv/dv)=6ve"+x(2v-1) O xv-(3v²+C)elt O None of the choices O…

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Q: Evaluate xe*dx. -3

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Q: The length of a rectangle is two-fifths of the radius of a circle. The radius of the circle is equal…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 3y2 + 2, (3, 5) Vf(3, 5) =

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5   As we know that; The expression for the gradient vector.…

Q: dx x'+3 Xん X

A: We have to solve the integral.

Q: 1. (3x²+ 2y²)dx + 2xydy=0 2. (x- 3y + 3)dx + (3x + y + 9)dy = 0

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the following limit by evaluating an appropriate definite integral over the interval [0, 1 lim…

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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