Evaluate / (x- 16)dA where Ris the region in the first quadrant enclosed between y = xand y = x². Round to two decimal places.

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. (y - x) dx +…

A: This is a problem related to integral of the function. Based on the general formula and concept we…

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 <ts 1. / (x+ 3y²) dy #4

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Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: 7. Solve the general solution of DE: y" -5y' + 4y = 3e%r O y = cje" + c2et* + er 10 O y = cje* +…

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Q: Describe the domain and range of the function. f(x, y) = 3x2 – y Domain: O (x, y): x = 0, y = o…

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = (V1 + V2, V1 - V2), v =…

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Q: 5. y!! + 2y! +v = 7+75sin2x

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Q: Exercises Repeated Roots of Auxiliary Equation Find the general solution of the following: 3. (4D2 –…

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Q: 13. r²/2 – 1 dx

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

Q: 2. Determine the area of the region bounded by the curve y = x³ – x² – 2x, and а. the x-axis b. the…

A: This is a problem related to area calculation using integration. Please find the procedure given…

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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Q: Find curl (8z i + 9x j+ 6y k). curl (8z i+ 9x j+ 6y k) = ( )i + ( i j + ( i )k

A: Find curl

Q: 13) Determine the lim X--9 + 169 く+9

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Barbara put P100 into banks savings account. The account accrues a 9% interest rate compounded…

A: Given: Amount =P100 . Rate of interest= 9%  Time n= 12 years

Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

Q: If f (x) : 2, what is the equation of the line tangent to f(x) at x = –1? O y+24x + 36 = 0 O y – 24x…

A: Given query is to find the equation of the tangent.

Q: y" + 2y' + 5y = 3 sin(2t)

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Q: 2. lim (ex – 1)lnx X0+

A: (2). The given limit is: limx→0+ex-1lnx As we know that, the second indeterminate form is: ±∞±∞ ;…

Q: 9) Given a piecewise function below 1 D)-2y/ n f(x) =] (1– x)× e -k (x>0) , Find lim f(x) = (x= 0)…

A: As we know from the the limit rule: If the limit is limx→afxgx and its result of the form of 1∞ then…

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x?y – 6xyz + 10yz2…

A: Given problem:- Find the first partial derivatives with respect to x, y, and z.   f(x, y, z) = 4x²y…

Q: Find curl (3z i + 4x j+ 7y k). curl (3z i+ 4x j+ 7y k) = ( i )i + ( i j+ ( )k

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Q: 7.) L13x + 1|dx

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: The integral TT tan x sec?x dx is an improper integral of type I that diverges is an improper…

A: To evaluate the following integral.∫π2π tan x sec2 x dx

Q: Find curl (6z i + 7x j+ 9y k). curl(6z i + 7x j + 9y k) = ( i )i + ( i )j + ( )k

A: Explanation of the answer is as follows

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = ti + t°j

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Q: 1- cos4x lim→0 5x e N – 1 O 1

A: This is 0/0 form so use L hospital rule and Solve.

Q: b. Vr4 – 2.x² + 1 dx

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Q: 47. f(x) = V(3 – x) on [1,3]

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Q: Evaluate the integral (12x + 12y)dx + (9x-y)dy along the parabolic arc y = x from (0,0) to (1,1).…

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Q: r=5 sin  18t  i−5 cos  18t  jr=5⁢ sin⁢  18⁢t⁢  i-5⁢ cos⁢ ⁢ 18⁢t⁢  ⁢j It is a circle of radius 1818…

A: We have to find the centre and radius of the circle.

Q: nd the general solution of the following: 2. (D3 – 4D² + 4D)y = 0 3. (4D2 – 6D + 1)y = 0 4. (25D2 –…

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: 3.) ž sin'(x)dx

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Q: O f(-1) = 3, lim f(x) = 3, lim f(x) = +∞ O f(-1) = 3, lim f(x) = -o∞, lim f(x) = +o0 O f(-1) = 1,…

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Q: Find V × (V × F) if F(x, y, z) = 9xyj+10xyz k. V x (V × F) =|

A: We have to find given expression.

Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Determine the vector field of F. (x, y) = 12i – 4j 1

A: given isF(x,y)=12i-4jgraph of vector field of F is attached below

Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

A: Given, y= sqrt(25-x²) y= 4

Q: Find fyry. f (x, y) = x°y® – 8a°y+x f yry ||

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Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

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

Q: Consider xy2+x2y=6, find the slope of the tangent line at the point (1, 2)

A: Given query is to find slope of the tangent at given point.

Q: I. Find the derivatives of the following 1. f(x) = 2x2 + 3x - 7 %3D

A: We know that ddxxn = nxn-1               and                    ddxpxn = p ddxxn = p× nxn-1 = pnxn-1

Q: Evaluate the double integral. 5x (4 + y)¯² dA; R R is the region in the first quadrant enclosed by y…

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Q: Using appropriate substitut tan³x dx sec5x is equal to

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Q: Without evaluating the constants, the partial fraction decomposition of 7x3 – 11 (4x3 + 7x2 +…

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Q: Find the absolute maximum and minimum values of f(x, y) = (x^2)y of the set D = {(x, y): x ≥ 0, y ≥…

A: To find the maxima and minima first diffrenciate and then equate it to zero.

Q: True or False. Explain your answer The limit of sin(x) as x approaches very large values is 0 or 1.

A: Given