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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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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: Solve the differential equation with the appropriate method. Finalize answer free of fractions,…

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Q: x(1-x')y = x' + y-2xy? ソ=

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: Use the series representation for cos x, cos x = 1 – + to find the following three items: 6! 1- A…

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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: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: This question is based on 3d line equation.

Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

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

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Q: Which of the following is TRUE if sin 3A = cos 6B, where 3A and 6B are complementary angles? * A + B…

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Q: In xdx

A: Formula:Integration by parts:∫ uv dx =u∫v dx -∫ dudx∫vdxdxI=∫ x5 ln x dxu=ln x, dudx=1xv=x5I=ln x ∫…

Q: Evaluate using Linear Equations. v(dx/dv)=6ve2v+x(2v-1)

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Q: If it is continuous, there are 3 conditions needed to be satisfied: i. f(a) is defined ii. lim x→a…

A: The three criterias that you have mentioned are for a point. When we check the continuity at a…

Q: Find the maxim um and minimu m value s of the the constraint x2 + y? + z? = 400. Maximum value is…

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Q: From a window 30 feet above the street, the angle of depression of the curb on the near side of the…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (5,13, -10) 2 tan(3)i,5…

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Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: dr Find if r sin[cos(-0)I. dr dr cos[sin(-0)] = sin 0 cos(cos 0) d0 d0 Option 3 Option 1 dr dr - sin…

A: The objective of the question is evaluate the derivative of the given function. Note -  As per our…

Q: Given f(x, y) differential df = 10x?y then the total O 20xy dx + 10x² dy 20x dx + x2 O 2xy dx + x²…

A: For the solution follow the next step.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

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Q: Find sin(2x), cos(2x), and tan(2x) using the given information. 7 csc(x) cos(x) < 0 2' -

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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: 4) represent the jollowing angles an higono metric cirde a7. + K2n 3. 4. c7 t. Eld

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Q: x'sec'ydy – (1 – 2x²tany)dx = 0

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Q: 4. The graph below depicts a function g(r). Its one asymptote is indicated in red: 4 -5 -4 -3 -2 -1…

A: Find your answer below

Q: Find the gradient of the function at the given poin w = x tan(y + z), (6, 15, –13) Vw(6, 15, –13) =

A: The given function is w=xtan(y+z) ............................................. (1)  We have to find…

Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 2. у — С1 3D С2е -4х 2. у —…

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Q: 6. Find the area of the region enclosed by the graphs of y = Vx+1 and y = }x – 2 and the vertical…

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Q: 2t2 + 38 sinh 16t

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given line x-38=y2=z-714=tAny point on the line is of the form,x=3+8t,y=2t,z=7+14t,Put…

Q: What is the edge of a cube whose volume is equal to that of a rectangular bar measuring 100 cmlong,…

A: Let the edge length of the cube be 'a' units

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

A: Given: f(x,y)=x2-2xy+y2, (5,7,4).

Q: x4

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Q: Evaluate the integral where D is the region bounded by y = x, y = 2, and r = 0. Hint: One order is…

A: We will solve this question by changing the order of Integration.

Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

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Q: Consider the function: f(x)=10√x+8 on the interval [1,8] .Find the average or mean slope of the…

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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: II Three graphs labeled I, II, and III are shown above. They are the graphs of f,f', and f".Which…

A: Observe the each curve using slope and increasing decreasing properties.

Q: where does this concave up and down?

A: A graph is concave up if f''x&gt;0 and concave down if f''x&lt;0. When f''x&gt;0, it means…

Q: The thermometer reading 700F is placed in an oven preheated to a constant temperature. After 1⁄2…

A: Given problem:- The thermometer reading 700F is placed in an oven preheated to a constant…

Q: 2. What is the slope of the line tangent to the curve 8x³ – y² = 4 at the point (1,-2)? 3. What is…

A: Since first subparts question statement missed. Answer 2 and 3

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 sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: Write the equation of the tangent line to the graph exy + cos v = + COS at He %3D point (-0.3, 2.12)

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Q: An approximation using four terms of a series for the number x3 cos (22) dx

A: Given:      ∫01x3cosx2dx MacLaurin series is given by            fx=∑k=0∞fkak!xk In our case…

Q: how about the equation of the normal line?

A: Apologies for the inconvenience. Here is the solution for the normal line:   From the original…