1. S cosxsin²x V1+sinx dx by algebraic substitution

Q: Find the lim inf (xn) and lim sup (x₂) of Xn = COS nπ

A: I have calculated the limits

Q: At what point in the first quadrant does the line with equation   y = 0.5 x + 4   intersect the…

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Q: Solve the initial value problem y" - 3y' — 40y = 0, y(0) = a, y′(0) = −35. Find a so that the…

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Q: [ 1² dx dy = 1/2 Select one: True False

A: Evaluating the definite integral

Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. Q -5-4-3-2 25- 20- 15- 10- 5-…

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Q: Solve the IVP: y" - 6y' + 8y = 0, y(0) = C

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Q: .1.2

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Q: Solve the problem. 10) Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 5.

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= X-2 9x-4…

A: topic- equation of tangent line to curve

Q: Find an equation for the ellipse whose graph is shown. y 0 (10,5) 15 X

A: Consider the ellipse  Consider the graph

Q: (2x - y)dx(x + 4y)dy = 0

A: As per the rules, we can answer only the first question and other can be reposted.

Q: 7. Convert the angle 5л 3 into degrees.

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Q: z² = √√√xe²y-x. Consider the surface described by the equation a Find the equations of the normal…

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Q: Compute /16-³ dac

A: Solution of given question is written in below steps.

Q: Without using a calculator, for the following, find rectangular coordinates for the given point in…

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Q: Consider the following. X+6 x²-x-42 Find the x-value (if any) at which is not continuous. Is the…

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Q: 8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥…

A: To eliminate the pararmeter to find a Cartesian equation of the curve: xt=t, and yt=3t+4, t≥0.To…

Q: lo 12-dxdy = (1 2* dx) (ody) Select one: O True O False

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Q: Question 1 1 a. [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) =…

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Q: 11. Calculate the Riemann Sum R(f, P, C) for f(x) {-3,0,2,5} = 2x + 3, P = {-4,-1, 1, 4,8}, C =

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Q: 3. State the remainder when f(x) = 2x² −x³ +1 is divided by (x+1).

A: We can find the remainder as below.

Q: Consider the following. lim 2x²-3x - 5 x--1 x + 1 Find the limit of the function (if it exists). (If…

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Q: II. Solve each of the given LDE of order n.

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Q: x² + y² - z² = 9 (u, v) = Determine the tangent plane at (3, 0, 0).

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Q: 7. Find the exact length of the curve: x (t) = 2t, y(t) = 2t, 0 ≤ t ≤ 1

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Q: gular coordinates √6 √2 2 2 (a) plot the poi

A: “Since you have posted multiple questions, we will solve the first question for you. To get the…

Q: The values of two functions, f and g, are given in a table. One, both, or neither of them may be…

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Q: = 0, y = x, and x = 5. n, the region D expressed as type I is: = {(x, y)|0 ≤ y ≤ x,0 ≤ x ≤ 5} ect…

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Q: Reversing the order of integration in the integral SS²ydydx equals: Select one: A. None of them B.…

A: Since you are asking multiple questions. We are answering only the very first question as per ous…

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 8. Convert the angle 315° into radians.

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Q: 1. Solve the differential equation: ² doc + 2xy = Inx, y (1) = 2

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Q: The equation of the tangent plane to the surface x2 at the point (-2, 1, 3) is Select one: +2y z-3…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: Use geometry to evaluate the definite integral. 8 26) Evaluate. 27) S 1 S (8 - x) dx x3. + 64 X + 4…

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Q: How many critical points the following function has, h(x, y) = 1 + x³ + x + xy²? Select one: O None…

A: We can find the answer as below.

Q: •√ (2x + √₁ (2r+√16-r²) dr by interpreting it in terms of areas. 10. Evaluate

A: Bh

Q: g and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal…

A: We will solve.

Q: Given f(x)=√x and g(x)=x²-1, evaluate each expression. (a) f(g(1)) (b) g((1)) (c) g((o))

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Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² − 2x³ + 3y² + 6xy. b. s]…

A: Given :fx,y=6x2-2x3+3y2+6xy

Q: True or False If determinant of matrix A is equal to 1, then the transposed matrix of cofactors of…

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Q: 5. What is the domain of the function h(x)= 11 X x 2 1 ?

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Q: ƒ(x) = [x] + [−x] teger function [x] is defined by the largest integer that is less es of a does lim…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

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Q: SPA 32 Select one: True ● False dx dy = 13 2

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Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation.…

A: The given cost function of producing x calculators is Cx=6+2x+48 , 0≤x≤50

Q: The function f(x, y) = -2x² + 4y? - 11 has a local minimum at the point (0, 0). Select one: O True O…

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Q: Match the vector-valued function with its graph. r(u, v) = ui + vj + uvk -2-1 2 2

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