1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ - 2x + 12 c) h(k) = 2-5k³ k² uborin

Q: · (b + c) = a · = a · b + a · e for all a, b, c € R³. . 7. Prove that a.

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Q: 1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement…

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Q: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

A: Given r = i cost cosht + j sint sinht

Q: Q6. Evaluate S¹, S₂ Sp dz dx dy.

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Q: 5. The movement of the crest of a wave is modelled with the function h(t) = 0.2 cos(4t) + 0.3…

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Q: Let f be a continuous function such that 2 Lª¸ ƒ(2) dx = - f(x) dx = -8. What is the value of -3 2…

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Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A: The given function is x2-y2+2xz-xy+yz.

Q: Use cylindrical coordinates to calculate: Sw(x² + y²) dV = [[[_x² + y²³ av W: x² + y² ≤64, 0≤ z ≤ 16

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Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: Find the flux of F across S, [/F. Nds where N is the upward unit normal vector to S. F(x, y, z) =…

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Q: 4. Which of the following functions grows at the same rate as 3^ as x g O 2x O√√3x +4 3* O √6x 0x +…

A: To compare the rate of growth between the given functions lets draw their graphs. Given function 3x,…

Q: 3. Including all steps, charts, and derivations details, use the curve sketching methods to sketch…

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Q: Find the indicated value. f(5,2) if f(x,y)=2x²y-5xy³ f (5,2)= 10 (Type an integer or a simplified…

A: Given a function fx,y=2x2y-5xy3 We have find the value of fx5,2 Derivative of a polynomial function…

Q: = Approximate the area under the curve y with 4 subdivisions. x³ from x = 2 to 4 using a Right…

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Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

A: Centerville is located at 10,0 in the xy-plane Springfield is at 0,5 Shelbyville is at 0,-5 The…

Q: Evaluate the definite integral. 1³ sin (4t)dt

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Q: Find the center and radius of the sphere with equation (z + 3)² + (y + 1)² + (z+4)² = 1 Center:…

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Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: Recall: Position vector v→=a, b where a=x2-x1 , b=y2-y1 We have (x1, y1)=(-6, 1) and (x2, y2)=(-5,…

Q: 60° IIPII=23 Q Find the EXACT components of the vector above using the angle shown. P Check Answer…

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Q: where does xk come from

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Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

A: Graph of the function given on the interval 2,4 with 20 sub interval of equal length we have to find…

Q: Evaluate the following indefinite integral. 1 √2 + 3x² Note: Don't forget your C! And be sure to use…

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Q: 2 1 Expand 2y 0.013 2 3. ✓0.0004:

A: Given problem:- Expand 2y210.013y2230.0004

Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

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Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform  thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: ³ [*₁ (32²¹ +42²) dz Find

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Q: Let v = 17 + 17 and w = 17 + 8j. Find a number c so that w- cv is perpendicular to v. C =

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Q: aluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any…

A: Given: rt= cost i + et j + t2 k

Q: Solve the differential equation (1 + y² + xy²) dx + (x²y + y + 2xy) dy = 0

A: Solve the exact differential equation  1+y2+xy2dx+x2y+y+2xydy=0

Q: Solve the differential equation dy dx y+√√x² + y² X ; when x x = a. y² = 2x-1 b. x² = 2y-1 2 c.…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the area of the parallelogram with adjacent sides u = (4, 3, 0) and v = (0, 3, 1).

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Q: y (2x + y 2) dx O a. y (2x + y) = Ce - 2(x + y) dy = 0

A: y2x+y-2dx-2(x+y)dy=0 Lets check for exactness.…

Q: Find a unit vector that is orthogonal to both = (1, 1, 9) and v = Enter vector brackets using the…

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Q: Find the cross product u x 7 where u = 2i -3j +k and = (7, - 3, 4). ü xü= Check Answer

A: We have u→=2i-3j+kor u→=2, -3, 1Alsov→=7, -3, 4

Q: π 7. fz sin¹x cos¹ x dx

A: To evaluate the following integral by using Walli's formula.∫0π2 sin4 x cos4 x dx

Q: 17.The volume of a parallelepiped is given by the following formula: a. c.(axb) Calculate the volume…

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Q: B A 876, 5432 -10-9-8-7-6 -54 -3 -2 -1 1234 -1 Graph of f D 1 2 3 4 5 6 7 8 9 10 C x.

A: We will find the required.

Q: 1. The graph of f '(x) is continuous and increasing with an x-intercept at x = 0. Which of the…

A: Topic- application of derivatives

Q: Problem 1. You are fencing in an area next to your house so your cats can lounge outside. The cat…

A: We have given the length of material that is avialble for fencing is 27 feet.

Q: Consider the revenue function R(x) and cost function C(x) for a company, given by…

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Q: What is the general solution to the the differential equationy'''=0? A y=C₁+C₁₂x 1 By=C₁+C₁₂x+C₁₂x²…

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Q: (a) Find an affine change of coordinates that takes the unit square with vertices in the uv-plane to…

A: (a) The vertices of uv-plane is given as , P*=0,0 , Q*=1,0 , R*=0,1 , S*=1,1 and the vertices of…

Q: x² yey lim(x,y)→(0,0) x4 + x + y²

A: To evaluate the following limit.limx, y→0, 0 x2yeyx4+x+y4

Q: Find 2 -1 (3x³ + 7x¹) dx

A: Here we have to solve definite integral

Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: We need to find vector.

Q: I have a question about the problem solved…

A: The explanation of your query can be solved using the concept of function.

Q: Find a formula for each function graphed below. a. b. (-1,4) -3 -5 (-4,-1) (1,2) (3,-2) O -3- (1,-2)…

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Q: Find the directional derivative of f at the given point in the direction indicated by angle f(x,y)…

A: Given function is: f(x,y)=excosy We have to find the directional derivative at the point (0,0) in…

Q: Find the work required to move an object in the force field F = (x,2) along the straight line from…

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