If = 27- 67 + 2k and y = i+3 - k, determine + 25.

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A: We can solve this as follows:

Q: Q2: State and prove the first isomorphism theorem.

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Q: The following integral may be solved using substitution. Choose a function u that may be used to…

A: This question is based on indefinite integral.

Q: sin(h) Evaluate: lim h →0 4h

A: Evaluating the limit with the help of standard limits.

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

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Q: 3. Determine if triangle ABC is a right triangle. Show and explain your work. A = (5, 6) B = (0, 2),…

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Q: in terms of x and y for the points (x, y) A5. (a) Use implicit differentiation to find that lie on…

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Q: || 21*y dA, R is bounded by the parabolas y = 3r* and y = 16 – r*.

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Q: S. 14 V1 + 7x dx

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Q: QI: A) Solve the following initial-value problem: x e* dx + (y- 1)dy = 0; y(0) = 0 %3D B) Solve the…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

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Q: For each of the following, determine whether the expression is positive; negative; or zero. (You may…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Q2: Solve the following linear differential equation: y' + y = x+

A: We can solve this as follows:

Q: If matrix B is obtained by multiplying matrix A one row or one column by a constant, then the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

A: We have to choose correct option

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: dy Find when 2x? + 3x°y – 3y3 = 32. dx dy dx The slope of the tangent line to this curve at the…

A: Take the derivative with respect to x using chain rule of derivative.

Q: Evaluate dx 2 1-x

A: We have to evaluate ∫23x1-xdx. We know that ∫dxx2-a2 = 12aln x-ax+a+C

Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f(x) = L = 1| 8 oProve that…

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Q: Find and classify the critical points of the function: f(z, y) = z' + y* – 144ry + 4 Local maximums:…

A: Given that; f(x,y) = x^4 + y^4 - 144xy + 4  Let's  find minimum and maximum points;

Q: Evaluate the following indefinite integral. dt t In(t) Note: Don't forget your C! And be sure to use…

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Q: 4) Evaluate each integral using the indicated substitution |(2x+7)(x² +7x +3)*5 dx; u=x² +7x+ 3

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Q: FIND THE DIVERGENCE AND CURL OF U = i (x 2+ yz)+j Cy?+Zx) t K (z?+xy] %3D

A: Given :u=i x2+yz+jy2+zx+kz2+xy.We need to find the divergence and curl of u.

Q: In R', the equation x² + y + z? = 4 describes a sphere of radius 2. Select one: True O False

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Q: complete

A: We will solve the integration.

Q: ) frnd the sum of the fitst 20tems în Grthimet senies the -6-12 18- A -2526 B -1266 Sn=g(aitan)…

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Q: A window consists of a rectangle surmounted by a semicircle. If the perimeter of the window is 32…

A: We have to calculate radius and height

Q: . Find the area of the region bounded by the two curves y = x3 + 3x2 + 2x and y = 2x? +4x.

A: As per Bartleby guidelines rule I am answering only first question because the second question is…

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A: We have to find the resultant vector.

Q: 1 х-x? dx -8 2 V

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Q: 8. Evaluate * y" – 3y' + 2y = e3t ; y(0) = y'(0) = 0 e2t -e3t + 2 et 23t -e2t + 2et 2 O A. e3t -e2t…

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Q: 3. Sy'edy

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Construct YOUR OWN example of how to determine the derivative of a given function and the process…

A: Given

Q: Find the tangent line to the curve y = x + 2x3-2x2 -3x + 3 which is perpendicular to the line x- 3y…

A: Given :y=x4+2x3-2x2-3x+3Line : x-3y=2

Q: please

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Q: (zx" xy') dx:-3xy dy

A: Given that a differential equations and we solve this problem by using general property of…

Q: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

A: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

Q: At low altitudes, the altitude of a skydiver and time in the air are linearly related. A skydiver…

A: Topic:   Linear Equation problem Here is the answer

Q: 8 Given a function: f(x) = (х-7)(х-1) Write down the definition that lim f (x) = L -1| х-5 (х-7)…

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Q: (zx" xy') dx-3xy dy 2-

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Q: 3-Find the area of the surface of revolution generated by revolving the curve y=V .1sxs3 about the…

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Q: 3. x = y? ,x = -2y² + 3

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Q: 3 Vx dx 2 x+1 Evaluate

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Q: 7. SYVY² +9dy 5-2 8. S (5-1)(s-5)(s+3) ds

A: We have to evaluate the given integrals.

Q: Find the area bounded 1. 2x2 + 4x + y = 0 , y = 2x 2. y = x³,y = 4x²

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Q: Q3): If x fx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n – 1)f %3D

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Q: Find the values of Xx, y and z that correspond to the critical point of the function: z = f(x, y) =…

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Q: Circle

A: