2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z = cosx by partial differentiation.

Q: 5. Two lines have equations: L₁: x = 3t + 1, y = 3, z = −t + 2, teR and L₂: x = 2s +3, y = −s + 1, z…

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Q: dx √3 1 + x²

A: we use the  formula ∫dx1+x2 = tan-1 x    +C

Q: 10 5 Let A 4 1 -3 k 6-2 Find the values of k for which A is invertible. O Ais invertible ifk # 27.2.…

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Q: Oil from a ruptured tanker spreads in a circular patter. If the radius of the circle is increasing…

A: Topic:- application of derivatives

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Q: Consider the following matrix. A = [22 -2] How many vectors are in the basis of row(A)?

A: Given: Now,                   30-3222Reduced matrix to reduced row echelon form:=10-1012The rank of…

Q: 6. Evaluate the following limits: 1/3 (x+8) -2 a. lim X x-0 b. lim x→-3 2 x²-9 2x² +7x+3

A: Given :limx→0x+813-2xlimx→-3x2-92x2+7x+3

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A: Above question is solved

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Q: An angle co-terminal to 19 6 11m 6 is

A: Given query is to find coterminal angle.

Q: 2. Raya Is making a closed rectangular jewelry box with a square base. She is using two different…

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Q: Solve the problem. Find the area between y = (x - 3)ex and the x-axis from x = 3 to x = 7. A) e²-e³…

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Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

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Q: 4. The point (0.422,-0.907) lies at the intersection of the unit circle and the terminal arm of an…

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Q: A wall lamp is positioned 7ft up a wall. A 6ft tall woman walks directly towards the light at a…

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Q: Suppose we have the points A = [0, 1], B = [1, 3], C = [2, 2] and D= [3,2] (you may have to move D…

A: answer is in next step . please give a like !!

Q: -3x₁ + x₂ + 3x3 = 0 -6x₁ + 3x₂ + 3x3 = 0 2x13x2 + 5x3 = 0 Write the solution set of the given…

A: The given system of equation,-3x1+x2+3x3=0-6x1+3x2+3x3=02x1-3x2+5x3=0

Q: 1. The graph of y=sin z is transformed so that the transformed image has a period of 4m and a phase…

A: Given problem:- The graph of y = sin x is transformed so that the transformed image has a period of…

Q: Find curl F if F(x,y,z) = 7exy i-8 cosy j +5 sin²z k. curl F = -7xexy k curl F = -7xexy i curl F =…

A: In this question, we want to find the curl of given vector function.

Q: Solve by Cramer's rule. X1 i X2¹ 6x1-2x2=4 3x1 + x2 = 10

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Q: Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by the…

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Q: 1) Solve a) log(x+4)=1 b) log, (2x-3)=2

A: Given problems :- log(x+4)=1  log5(2x-3)=2

Q: Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p…

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Q: Find the inflection point of the following function, if any: y = x(x - 5)¹/5

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Q: Which of the following equations is(are) true? 1 2x du I. -dx x² + 1 S 5.² o √u √2 1 2x II. -dx 10…

A: Given: I=∫012xx2+1dx   ...1

Q: Determine whether the differential equation (2x² − 2xy + 3) dx + (7y² − x² + 2) dy = 0 is exact. If…

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Q: Let 7' (t) = Find a parametric equation of the line tangent to r(t) at the point (59, 0, - 2.303)…

A: Follow the procedure given below.

Q: x-p In the table, Y, is defined by a rational function of the form p= Use the table to find the…

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Q: The power series n=1 0-1≤ x < 5 01≤x≤5 0-1 < x < 5 0-1≤x≤5 (x - 2)" 3n converges if

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Q: 2.)fedxdy

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Q: Solve for x sin(log2 (13x² +16x34) = y

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Q: Q1: A. Find the general solution of the following Initial Value Problem (IVP): y-2y-3y=e²t 8. Find a…

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Q: Solve the following integrals: 1. f-7e*dx 2. (2ex-6x) dx √(3¹) dx 3. 4. f 8x+1dx 5. f=dx X 6.…

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Q: a) 4x²y - 3xy³ + 6x; d) e²x+3y; b) xy; e) x+y x-y c) xy²; f) 3x²y-7x√y.

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Q: 0,4) A B) 3 C) 5 D 23 5 गज 2 C 11 A - x² 3 (3,-5)

A: Topic:- application of integration

Q: Find :a. b. 20 fő -1 20 dy (1+y) ² (20-6x) e 20x - 3x² dx

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Q: Nx - My If = R, where R is a function depending only on the quantity z = xy, then the differential…

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Q: an isosceles triangle! 9. Find an equation of the sphere that passes through the point (4,3,-1) and…

A: Given problems:- 9. Find an equation of the sphere that passes through the point (4,3,-1) and has…

Q: Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p…

A: "According to the guidelines issued by the company we are supposed to answer only first three…

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Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight…

A: Given problem:- A lighthouse is located on a small island 4 km away from the nearest point P on a…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: We have to find position vector

Q: b. √x+√9-5x²dx

A: Topic:- integration

Q: a.find the slope of the line tangent to the graph of f at P. b. Determine an equation of the tangent…

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Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

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Q: 1 X x2 – a 2 dx

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Q: Q4- Solve the following differential equation: (1 + x²) dy + (y - tan-¹(x)) dx

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Q: The area of an equilateral triangle with sides of length x is given by the function √3 defined by…

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Q: Example 4: Find the equation of the plane through the point (-4, 3, 1) that is perpendicular the…

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