Q5: A. By power series, solve the ODE y' - 2xy = 0.

Q: Find a,b to continue the function at x=3 if: x > 3) x = 3 x < f(x) = ax + b 2ab + 1 bx - a +3 3)

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Q: (6) Set up but do not evaluate the integral representing the volume of the region (circular…

A: Given Ellipse, ax2+by2=r2That isby2=r2-ax2y2=1b(r2-ax2) ax2+by2=r2Divide r2 on both…

Q: At what points is the following function continuous? 3 x - 125 x²2²-25 f(x) = 7.5, 4, X#5, x# -5 x =…

A: Given function:- fx=x3-125x2-25x≠5,x≠-57.5x=54x=-5 Condition for continuity at x=a…

Q: 316. [T] The graph of a folium of Descartes with equation 2x³ + 2y³ - 9xy = 0 is given in the…

A: This question can be solved using the concept of equation of tangent and normal to the given curve…

Q: If f(x)=x²+4, find f(x +h)-f(x) and simplify. f(x+h)-f(x) =

A: Given query is to perform indicated function operation and simplify.

Q: f(x)=(x-6)³+4, [4,7],f(c)=3 3

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Q: the derivative. 28) y = x5/6 A) 5x7/6 B)x1/5 a C)/x-5/6 D) Ex-1/6

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

Q: Differentiate. g(x) = 4x-9 5x+1 g'(x)= 3 + X

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Q: f(x) = 4x2 − x + 2,  find the following.

A: Solution is given below:

Q: 2. Let u=i+aj +3k and y=2i-3j+ ßk i. ii. iii. If u is parallel to y, find the values of a and B Find…

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Q: Find the decomposition a = ªb + ªь with respect to b if a = (x, y, z), b = (-1,-1,-1). (Give your…

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Q: sine = COSA coto || || || |||| CSCD= sec 0 =

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Q: K False 3. True or False? An independent variable represents the range value or output of a…

A: To write down that the given statement is true or false.

Q: (d) y' = x(1 + y²), y=tan(\x²)

A: Solution of the differential equation satisfy  the differential equation

Q: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

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Q: Suppose ū = (–5, −4, −5) and v = (–2, 4, −5). Then u x vis Uxuis and

A: Topic- Cross Product of Vectors

Q: 6. x = c₁ cos tot + c₂ sin cot; w a parameter.

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Q: Write an equation for a rat Vertical asym Enclose numerators and de Include a multiplication sign…

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Q: 2. In 2000, Morgantown's population was 26,800. It's population increases by 1.2% each year. a.…

A: Solve

Q: Given the graph of f(x) = x² as shown, graph the function - 5ƒ(x + 4). 10+ 9+ 8+ 7+ 6+ 5- 4+ 3+ 2+…

A: The function is fx = x2 The graph of the function is To evaluate: The graph of the function -5fx+4

Q: A. Write ✓ on the line if the given equation is a circle; otherwise write x. If the equation defines…

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Q: Prove that tan'z= let% 1/2 in (1+2) ة لله tan't Z • tanw=Z Z = Sinw cosw

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Q: 1) f(x) = *-1 x+2 Find a) f(1) b) f(a + 1)

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.

Q: For each equation, solve for each variable in terms of the other variables. y=z/x For example: z =…

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Q: Find the domain of the rational function.

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Q: Find the distance from the point (1, 5, 5) to the line x = 0, y = 5 + t, z = 5 + 5t.

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Q: 3) Determine the speed of change of volume of a rectangular parallelepiped, knowing that the edges…

A: Let the length of base edges and vertical edge are x, y and z respectively such that dxdt = +2…

Q: Find the area of : y: 4/x, y-4/x2, x=6

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Q: r₁(t) = (14,3, 11) + t (−4, −1, −3) r₂(t) = (0.5, 4, −11) + t (1, 2, −4) Find the point of…

A: Given: Equations of lines:r1(t)=14,3,11+t-4,-1,-3r2(t)=0.5,4,-11+t1,2,-4

Q: In each of Problems 1 through 8: Ga. Draw a direction field for the given differential equation. b.…

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Q: (a) If the point (1, 7) is on the graph of an even function, what other point must also be on the…

A: Topic- functions for even function if (x,y) is on the graph then (-x,y) is also on the graph for odd…

Q: For each statement,write true or false {0,2,6}={6,2,0} {2,3,4} =[2,4] {XER:0≤x≤6}= [0,6]…

A: We will  state whether the statement is true or false.

Q: 7. A traditional first experiment in a physics laboratory is to make 98 observations ab records the…

A: Given formula for linear regression is as below  take t as x and h as y. find mean value

Q: 3. lim_ f(x) = X-3- lim f(x) = X-3+ lim f(x) = x-3 f(3) =

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Q: 1) Find the difference quotient of f(x)=x². That is, find f(x+h)-f(x) for h#0. Simplify so h that h…

A: To find the difference quotient of the given function.

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: 2. Show that the function f(x) = xsinx has in infinite number of Critical Points by doing the…

A: The given function is : f(x)=xsinx Now finding the derivative f'(x) :

Q: n=1 1 n√n

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Q: Find any vertical asymptotes of the function: f(x) = x-4 x² - 4x - 45 Write the equation of the…

A: The given function is: fx=x-4x2-4x-45   As we know that; To calculate the vertical asymptote, equate…

Q: Find the limit x-5 lim x→5 x²-25

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Q: 4. Evaluate: lim(x² - 10x) x→6

A: This question can be solved by replacing x by 6 in the expression x2-10x.

Q: Find any vertical asymptotes of the function: 7 e² - 5 f(x)= 1 Write the equation with the lowest…

A: The given function is : f(x)=7ex-5

Q: 13. The rate at which a garden uses water is measuued in thousands of gallons. If the usage rate is…

A: I am attaching image so that you understand each and every step. Given data:- The rate at which a…

Q: Is the function g(x) continuous at x = 5? g(x)= O No 1 5X+7, 5x-13, for x>5 Choose the correct…

A: Given query is to find function is continuous or not at x = 5.

Q: Find the value of c such that the function is continuous on the entire real number line. f(x)=…

A: Topic = Functions

Q: Find the domain of the function. (Enter your answer using interval notation.) G(x): 8x + x X Sketch…

A: Solution ) G(x) = (8x + |x| )/x G(x) = 8x/x + |x|/x  G(x) = 8 + |x|/x  If x = 0 G(x) = 8 + 0 = 0 If…

Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: Find the value of a, b, c, and d. Enter all answers in exact, reduced form. No decimals are allowed.…

A: Please refer to the image below

Q: A wheel of radius 14 inches is rotating 12°/sec. What is the linear speed in in/sec and the angular…

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