Find div F and curl F if F(x, y, z) = 10y°2³i – 11x°z!°j – 3xy°k. „10: div F= curl F=

Q: Determine the limit of the sequence or state that the sequence diverges. n an = Vn3 + 2 (Use…

A: Given: an=nn3+2 To find:  limn→∞ an limn→∞an=limn→∞nn3+2 Given limit is of ∞∞ form

Q: Given x sin 4t and y = cos 4t, find the following derivatives as functions of t .

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Q: Find curl (9z i+ 10xj+ 2y k). curl (9z i+ 10x j + 2y k) = ( i Di + ( i j+ ( i )k

A: We have to find the curl

Q: Find the indefinite integral using the substitution x = 5 tan(0). (Use C for the constant of…

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Q: Solve the following differential equations of dy 1 y= xy': + dx

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Q: Find the area of the shaded region. y=x-4 y= /2x 2. 8. 10 x -4 2.

A: Given query is to find the area of tha shaded region.

Q: An Easter ham is put in the oven with a temperature probe embedded in the center. Assume the…

A: We are given that, an Easter ham whose temperature is 40° is kept in an ovan whose temperature is…

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: We use the concept of derivatives to find the absolute minimum and absolute Maxima

Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

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Q: Consider the function f(x) on the interval [1, 11]. Find the average or mean slope of the function…

A: Given,  f(x)=1x

Q: A ball is thrown into the air and its position is given by h(t) = - t² + 85t + 2 where h is the…

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Q: In t years, the population of a certain city grows from 700,000 to a size P given by P(t)= 700,000 +…

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Q: 2.x4 + x3 x4 xp-

A: Given query is to find the value of the integral.

Q: a" + C,C E R. In a If a is any positive number except 1, then a" du True False

A: The given statement is True.The exception exist at a=1 because then in denominator we will have ln1…

Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (v 36 –…

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Q: 2. Let f(x) = VI(2 – x)². Use the local linear approximation of f(x) at ro = 1 to estimate V0.99…

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: Find V (F x G), if F(x, y, z) = 11xi +j+ 13yk and G(x, y, z) = xi + yj – zk. V. (F x G) =

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Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

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Q: Consider the following equations. f(y) %3D У(5 — у) g(y) = -y

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Q: Oil is leaking out of a ruptured tanker at the rate of r(t)=40e^(-0.03t) thousand liters per minute.…

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Q: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[8t^2 e^-2t]

A: Laplace transform of the function f(x)Lf(t)=∫0∞e-stf(t)dt

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Find the value of the specified finite sum. Given ak = 3 and bk = 7, find (ak- 2bk). %3D k=1 k=1 k=1

A: We can find the specified finite sum as below.

Q: A 15-kg quantity of a radioactive isotope decays to 7 kg after 11 years. Find the decay constant of…

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Q: 225 ft X A building that is 225 feet tall casts a shadow of various lengths as the day goes by. An…

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Q: Answer each question appropriately. f(x) dx = 9. Find -2 f(x) dx , if f is odd. Suppose that

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Q: Let f be a function admitting continuous second partial derivatives, about which it is known that:…

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Q: Find: W(e2x, –5e3x) A. 5e3x B. 4e5x C. -5e5x D. -4e* E. None

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Q: Show that \{e ^ (- x), x * e ^ (- x)\} is a fundamental set of solutions of y^ prime prime +2y^…

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Q: 3x + 4y – 5z= - 8 4x + y- z= - 14 x- 3y + 3z = - 10

A: answer is in next step

Q: Evaluate the line integral | -ydx + xdy along the curve C:y? 30x from (30, 30) to (0,0). NOTE: Enter…

A: We need to find integral.

Q: The curved portion of the v-t curve shown in the figure are second degree parabolas with horizontal…

A: answer is in next step

Q: A company that produces cell phones has a cost function of C = 6x² – 197x + 1859, where C is the…

A: C= 6x2-197x+1859differentiating w.r.t xC'=12x-197+0C'=012x-197=0x=19712

Q: Find curl (3z i + 4x j + 7y k). curl(3z i + 4x j + 7y k) = ( i Di + ( i Oj + ( )k

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Q: If y = xe'* is a solution of a linear homogeneous 2nd order DE, then another solution might be A. y…

A: For a second order linear homogenous equations, If roots of auxiliary equation are 1. real and…

Q: 2 Integrate | 20(5æ – 3)°dæ - – 2

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Q: 22 r = 7 sin 0 + 50 cos O

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Q: The surface S is parametrized by equations x = u + v, y = 3u?, z = u – v; The point P (2, 3, 0) lies…

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Q: Let L be the line r(t)=(1+1,1-2r,3+5t) and II be the plane 2x-y+3z-48=0. a Find the point of…

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Q: What is the area of the region bounded by the graphs of y = x – 2x and y = -x+2? %3D - %3D O A =…

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Q: Use linear approximation, i.e. the tangent line, to approximate V1.3 as follows: Let f(r) = VT. The…

A: f(x)=x3f(x)=x13differentiating w.r.t xf'(x)=13x-23value of m at x=1f'(1)=131-23=13f'(1)=13m=13at…

Q: B. Find the area of the region bounded by the following:

A: answer is in next step

Q: /1 5/2 Find the length of the curve r (t) = ( t,4t,25t ) for 0<t <1.

A: Use the parameterization of curve for finding the length of curve .

Q: Evaluate | (2x – y) dx + (x + 5y) dy. C: x-axis from (0, 0) to (0, -5) and (0, -5) to (8, -5) -80

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Q: Kuya Bill is selling 'Bill phones'. If the cost for selling r phones is given by 10000 C(r) = 120x +…

A: Given, Cost function, C(x) = 120x + 10000/x - 2000 Price Dand function, p(x) = 1000 - 2000/x2 + 200x

Q: S 289 xe

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Q: a) Graph the function f(x) = 2x -5x+3 b) Draw a tangent line to the graph at the point whose…

A: Given the function is  f(x) = 2x2-5x+3

Q: 2)Consider the parent function y = x^2. For each function below, describe the transformations which…

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Q: Find ke ende finite integral. cuse c for Ge Constant of entyration) J Sin 39 Jcos 34 de (the + are…

A: We need to solve integral.