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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 3yz²k; (2,…

A: This question is based on divergence of vector.

Q: r(t) = (tan(5t))i+t cos(t)j – Vtk

A: Given: rt=tan-15ti+tcostj-tk

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

A: limt→2t3-7t2+16t-12t4-4t3+4t2

Q: dy Given a first order differential equation dx Зx* у + tan y x' +xsec' y Q3

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Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

A: The given plane curve is   x2+y2 =16.  We have to represent the curve by a vector valued function…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) arcos…

A: Givencos-1cos-3π2We know…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find the domain for given vectorr(t)=cosπti-lntj+t-2kand also to find rt0, t0=3

Q: Use the Rules of Differentiation to differentiate the following functions: a. f(x) = 2x³+ 6x d. h(x)…

A: Given data

Q: Q2) Find the integral of: 6 tan*x dx

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Q: d Calculate r:(t) - r2(t)] and r:(t) x r2(t)] first by differentiating [ri(t) × r2(t)] first by…

A: Given that     r1(t) = cos(t)i + sin(t)j + 8tk    r2(t) = 7i + tk

Q: (-5 S + (0.9)" | lim

A: Given query is to find the value of the indicated expression.

Q: Determine if the following function is continuous or discontinuous at x = 0? 4 +5 f(z) = 9-3z

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Q: 2. S CoSx+sinx-1

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Q: 3 of 20 Select the best answer. (2e + 1)ª lim z+00 (tan(x))- O DNE

A: We have to find the limit.

Q: Calculate the limit of the following recursive sequence ao = 1 an+1 = V1+ an Hint: Prove that an is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3. (D² + 1)y = sec² x tan x. %3D

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Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: cos2x dx sinx

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Q: 10 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx=5 . 8. (A) True (B) False

A: To determine whether the given statement is true or false.

Q: Evaluate the definite integral. O e10 e10 - 1 i+ k 10 10 - 1) j+ k 1- e10 - 1 10 e10 i - e j+ 1 k 2…

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Q: Cives f(x.g) = メー2メラーリメy+5 Find the Ccritical points oo f and all detevmine the nature of each of…

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Q: The point is on the terminal side of an angle in standard position. Find the exact values of the six…

A: Given that the point is on the terminal side of an angle in standard position. To find the exact…

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: 1. Let -1 -5] 3 -7 3 -6 -3 A = B= 6. 5 -3 -2 4 2 | -3 Determine which (if any) of the following…

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Q: Q5) Find the integration by using (by part method): Se3x sin X dX

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Q: Suppose that f(r, y) ry. The directional derivative of f(x, y) in the directional (1, - 1) and at…

A: directional derivative f(x,y) = adf/dx +bdf/dy (a,b) = (1,-1) df/dx = y df/dy = x directional…

Q: In(x) -dr

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Q: If z = 52? – 3y? + 4y, find the differential dz. You should have variables dz, dy, y, and z in your…

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Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

Q: Find V (V x F), if F(x, y, z) = 6ei+ 9xe'j - 5e k. V. (V x F) = %3D

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Q: dx sinxtanx

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Q: Зx* у + tan y dy Given a first order differential equation dx x³ +x sec? y (a) Clarify the exactness…

A: To solve the given differential equation

Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: ||r'(t) × r"(t)|| Use the formula k(t) : to find k(t). ||r'(t)||* r(t) = t’i + t®j 390 t14 K(t) = t3…

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Q: differential cgnatuin as A. Identify the given to the dependent variable, degce z the eguati degre 3…

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Q: xー1 dx (x+1) (x-3)5

A: Use substitution method for solving the  integral.

Q: ) (2xy+y2) dx - 2x2 dy = o 2) xy dx-(x + zy)? dy = o メ+ 2y)? dy

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Q: 1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the…

A: Given: x29-y216=1

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: by which criteria?

A: Apologies for the inconvenience. Here is the correct solution.   If a series ∑n=1∞an has either…

Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: xdx 46. S- V3+2x². – x+

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Q: 6. Find equations of the tangent line and the normal line to the curve y = 1+ x2 at the point (1,)…

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Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x² – 9…

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Q: xdx 41. 12-х

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…