1. Use a Trigonometric substitution to evaluate the following: Vy² – 25 -dy,y > 5 y Include a sketch of the triangle illustrating your tig substitution(s).

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

A: use the definition  of exact or non exact.

Q: In cach of the following, write the matrix A as a product SDS, where D is a diagonal matrix. ( ) 10…

A: We have to diagnose the above matrix.

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

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Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: Evaluate by separation of variables. dB u(1 – u?) sec² ß | du

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Q: 5. * 1 dx х (In x)3 1 + C 2 (In x)² 1 + C 3 (In x)2 A C 1 + C 2 (In x)? B D z+C 3 (In x) O A В E…

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Q: b/ Find the solution to the homogeneous differential equation below dy x²+y² dx 2xy

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Q: 1 dx V16 – x²

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Q: 3 A body moves along a horizontal line in accordance to s t + 912 + 24t. Find the total distance…

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Q: If a cylinder, a hemisphere and a cone stand on equal bases and have the same heights, what wil be…

A: Cylinder, Hemisphere and Cone have same bases i.e. all three have same radii (say r) Also the height…

Q: 3. y = ln³(x + sin x) 4. y = tan¬1(3x) cos 1 4x G ED DI 5. y =

A: All the questions are a solved below.

Q: 1. 9. 2

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Q: The graph shown below is fx) = x + 1. What is the integral function g(t) that defines the area under…

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Q: What is the x-intercept of the tangent line to y=ln(x) with a slope of 8?

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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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: 18. lim x+oo 3 20. lim log,

A: Given function f(x)=log12 x we write    log10 x=  log x     and we know thhat    log10 10=1

Q: 40-4V-V v? du

A: ∫40-4v-v2 dv∫44-4-4v-v2 dv∫44-4+4v+v2 dv∫44-22+2(2)v+v2 dv∫44-v+22 dv∫2112-v+22 dv

Q: 1- use Gauss Elimination to solve the following set of equations: 3x-y+z=-2 x+5y+2z=6 2x+3y+z=0

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Q: dy Find for the following expressions: dx а) y = x³ In(3x) b) y = 2 cos (+ 2x3) X 3x2 + 7x + cos (x)…

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Q: Solve the given initial-value problems. te dx +(y-1)dy=0; y(0) 0 4.43.

A: identify the differential equation and solve it.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

A: Given problem:- Find an equation of the tangent plane to the surface at the given point. f(x, y) =…

Q: Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and the…

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Q: 2. Find the center of mass of the four particles having masses 2, 3, 3, and 4 kg and located at the…

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Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

A: In this question, we want to find an equation of a sphere which is concentric with the given sphere.

Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

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Q: x'sec'ydy – (1 – 2x²tany)dx = 0

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Q: Determine whether u and v are orthogonal, parallel, or neither. u =j + 8k v = i - 6j - k

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

Q: Evaluate by separation of variables. dB du = u(1 – u²) sec 3 O 2u? + sin 28 = C – (1 – u²)² O 2 sec…

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Q: S 3xe*dx

A: Given problem :- ∫ 3xex/2 dx

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: An ice cream cone is filled with ice cream and surmounted ice cream in the formof a hemisphere on…

A: Given problem:- An ice cream cone is filled with ice cream and surmounted ice cream in the form of a…

Q: Consider the expression (3x² + 2/x)10 a) Find a simplified formula for the general term. (separate…

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Q: 1. Determine whether the following integrals converge. (a) 1 dx x3

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Q: Let A be the area of a circle with radius r. If dr/dt=5, find dA/dt when  r=2.

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Q: 2z2 + 7z +4 Let f(z) = 1³ + 2x² + 2z [1] (a) Write the general form of the partial fraction…

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Q: Answer the following True or False. If f(x)dx 0 and f(x) is continuous, then a = b. O True O False

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Q: A number is one more than thrice the other number. What is the minimum product of the two numbers?…

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Q: Integral Calculus: Integration by Parts (Original method

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Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: To determine whether the given function is homogeneous or not.

Q: Solve the following system of PDES. Uzz = 0, Uzy = 0 0, uzy = 0

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Q: ind general solution by separating the v y3 = (y* + 1) cos x %3D dx.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: On which interval is the function increasing? * 40- 20- 2. 20- -40- O (- 3, 3) O (3, 5) (- 5, - 3) O…

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Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: ) Find: dx/dt  at  x=−4  if  y=−3x^2−2  and dy/dt=1. dx/dt=

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Q: If f(r)dr = f(x)dr+ | f(z)dr - f(r)dr. 7. what are the bounds of integration for the first integral?…

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Q: s the volume of the frustum of a cone whose upper base is 16 cm in er, lower base 10 cmin diameter,…

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Q: Where is the function decreasing? * (-1,3) (-2,1) (0,1) O (*-1) O (*, *) O (-1, ) O (-*, 3)

A: A function is said to be decreasing in an interval in which on increasing the value of x, the value…

Q: Block A is sliding across a horizontal and frictionless surface when it collides with block B as…

A: We have to find the initial speed of block A.