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

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

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Q: Verify the integration formula. S 6 sechx dx = tan-1 (sinh 6x) + C (A) No B) Yes

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Q: t3 sin 8t

A: Given problem:- t3 sin(8t)  To find:- Laplace Transformation of given function

Q: Solve the following items and show your solutions. c.) Find the general solution and solve for the…

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Q: Direction: Find the differential equation of the family of curves described. 5. Circles with fixed…

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(1,…

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Q: 3dt 1. (2t+8) Vt+1

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Q: Consider the function y = 3(square root of x) + 8. What is the value of C in the interval [4, 9]…

A: First we will find fave

Q: Determine whether the planes are parallel, orthogonal, or neither. 4x – 20y – 4z = 4 3x – 15y – 3z =…

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Q: ds Find the function s(t) satisfying = 4 -9 cos t and s(0) = 7. dt

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Q: Evaluate using Linear Equations. v(dx/dv)=6ve²"+x(2v-1)

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Q: Question Using Partial Fraction Method, evaluate: S (1 + dx х2-1. Your answer

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Q: 2. Solve the given the equation using the integrating factors found by inspection. [2х + усos(ху)jdx…

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Q: 2pq If sin A = ,where A is an acute p2+q² • angle of a right triangle, what is sec A? p² + q? p² +…

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Q: The equation of the line tangent to the differentiable and invertible function f(x) at the point (5,…

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Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

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Q: After a rest of 20 minutes the hikers ascend into a steep climb, still following the trajectory of…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: - Find the Taylor series expansion for the given function about x =g. :- Using the Taylor series…

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Q: true or false 1. ∫dx/(1 - 2x) = 1/2 ln|1 - 2x| + C 2. ∫ (1 - 4x4 + x3)/x3 dx = 1/(2x2) + 2x2 - x…

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Q: Find the volume of the region lying above the cone o = and below the sphere p = 7. (Use symbolic…

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Q: Solve the initial value problem. d?r 2 dr = 5, r(1) = 4 dt2 dt t=3

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Q: Evaluate xe*dx. -3

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: We can solve the given problem as follows:

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: Use the cylindrical shell method to calculate the volume of the solid formed by rotating the graph…

A: Cylindrical shell Method : The Volume of the solid obtained by rotating about the y-axis the region…

Q: Which of the following is not equivalent to tan"? 2 1- cos 0 csc 0 + cot 0 sin 8 O Option 1 O Option…

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Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

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Q: 5 If csc² A = ;, what is the value of 1- cos? A? 2 5 5 2 2 Option 1 O Option 2 2 2 D Option 3 O…

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Q: In trigonometric substitution where the integral involves va? + u², what must be the value of the…

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Q: e length and breadth of the floor of a room are 30 ft. and 20 ft. pectively. Square tiles of 2 ft.…

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Q: Find the gradient of the function at the given point. f(r, y) = 3x+52 +1, (2, 1) %3D O 3i+10 O 3i+5j…

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Q: dx V3+2x-x2 10.

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Q: How do you take the integral of sqrt(1+(e^-x)^2)?

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Q: A CAT scan produces equally spaced cross-sectional views of a human organ that provide information…

A: Given information:  The x-sectional area of liver is given at interval of 1.5 cm. Note : The figure…

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: Solve the following items and show your solutions. c.) Find the general solution and solve for the…

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Q: is given by: If f(x, y) then 8(8x-4y) '

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Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: Use the cylindrical shell method to calculate the volume of the solid formed by rotating the graph…

A: To solve the following problem

Q: 1 a. f(x)3D 4 b. g(x) = - X c. h(x) = 3 -

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Q: Q4: Evaluate each of the following integrals: (a) | (4+ cos x)· sin x dx (Substitution)

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Q: ind the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: Given: u=3  θu=8v=1 θv=3

Q: Consider the function y = 5x4-4x3-3x2+8x-12. What is the average value of the function on [-3, 1] ?

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Q: Find dx and simplify whenever possible. 1-cosh x 1. у 3D 1+cosh x 2. y = x tanh¯x + In V1 – x²

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Q: (3 - 2 3 – 4cos dx

A: The given integration,     ∫3-4cosxπ2 dx

Q: What is the amount of material in a hollow cylinder of height 20 cm, given that the sum of the…

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Q: The graph of fis shown. Evaluate each integral by interpreting it in terms of areas. y y= fx) 6. 0.…

A: Given query is to find the value of the integral.

Q: Direction: Solve the following equations using separation of variables. 2. y' = x(1+ y²)

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Q: Determine whether each point lies on the line. x = -2 + t, y = 4t, z = 5 + t (a) (0, 8, 7) O Yes No…

A: topic - lines and points