Find the sum A+B+C of the constants A,B and C appearing in the Taylor series expansion given below: 9+ 72 sin(3z + 7) = A+ B(x – ² + C(z – * +.. Answer:

Q: 1(10,15) 2. An ant farm population is growing at a rate of g()=15e and declining at a rate of…

A: The rate of growth of an ant farm is gt=15e5t and  the rate of decline of the ant farm is dt=15e5t.

Q: Q2) Convert the polar function r tan20 to cartesian. %3D

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Q: Determine whether the integral is improper (x- 4) -'dx

A: Step 1: Identify whether one or both of the bounds is infinite. If so, then this is a Type I…

Q: dy Find dx of æ³ – y? = 5 by implicit - differentiation and evaluate the derivative at this point:…

A: According to our guidelines, we can answer only one question or three subparts of a question, other…

Q: Approximate the integral using Taylor series method: | xsin?x dx

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Q: Let f(r) = 5I + 2. Using the definition of derivative at a point, a. enter the expression needed to…

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Q: d d Calculate ri(t) · r2(t)] and r(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t < v2 In 5 NOTE: Enter the exact…

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Q: Find the marginal profit function if cost and revenue are given by C(x) = 184 +0.3x and R(x) =…

A: This is a problem of differentiation . Based on the formula and concept we will answer the question.

Q: Conjecture a formula for f'(a) that depends only on the value a. That is, in the same way that we…

A: Given that, fx=4x-x2 We need to compute the value of f'a.

Q: APProximate the area under fa)=XZ 1. and a 1.9ht approXimation cright end Point reltungies 100 k…

A:

Q: 13. Find the mass of a thin funnel in the shape of a cone z = x² + y²,1<z< 4, if its density…

A: It is given that, the equation of a cone is z=x2+y2,1≤z≤4 and the density function is δx,y,z=10-z.…

Q: Determine whether the integral is improper (x-4) -'dx A Improper B Not improper

A: Given data÷

Q: Find the arc length of the polar curve described by: r = 5+ 5 cos 0

A: Use the formula for the arc length in polar coordinate.

Q: 3. At 2:00P.M, a thermometer reading is 80°F is taken outside where the air temperature is 20°F. At…

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Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

A: Given parametric equations of a curve.

Q: Q2) Find the integral value for the following functions 3x 1. S V1+3x2 dx 2. S(sec(4x) – 1)? dx dx…

A: LetI=∫3x1+3x2dxTake the constant out:  ∫a·fxdx=a·∫fxI=3·∫x1+3x2dxPut…

Q: e consider the non-homogeneous problem y" +4y =-32(3x + 2) First we consider the homogeneous problem…

A: We need to solve IVP.

Q: B) Find for the Implicit function: dx x? – sin(xy) + y? = 5xy

A: The given equation is; x2-sin(xy)+y2=5xy.

Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

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Q: Verify Green's Theorem by evaluating both integrals aN y? dx + x² dy = /, J da ay ax for the given…

A: We have to verify the green theorem for the

Q: Find the exact arc length of the curve over the stated interval. y = 3r/2 – 4, from z = 0 to r = 1…

A: The curve y=3x32-4, from x=0 to x=1

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: 1. a dx 2. f(sec(4x)- 1)² dx 3. S 1+(Sx+1) dx

A: As per our guidelines, we are supposed to answer only the first three parts. Kindly repost other…

Q: 1. a) Find the linear approximation of f(x) = Vx at x= 27 %3D b) Use it to approximate V26.9

A: To find linear approximation of given function

Q: Question 7 Find the area enclosed by the curves y=2r², y=2\/x,x=- and x = 1 A 45/51 B 59/76 49/96…

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Q: An individual needs a daily supplement of at least 312 units of vitamin C and 170 of vitamin E and…

A: Let, the amount of food I be x ounces.and, the amount of food II be y ounces. as the quantity of…

Q: t or points for each ase portrait on this page. dx = 2x – 2y – 4 and- = x+ 4y +3 dt dt GURE 6.1.

A: Given

Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

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Q: dy + 3x2 + 2y3 = 0 dx e) Solve (6x + 1)y?

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Q: 4 Find the inverse Laplace transform of s? + 8s

A: As we know from the property of the Laplace transform; L-1a·fs+b·gs=a·L-1fs+b·L-1gs And…

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: If 10% of a radioactive substance disintegrates in 4 days, what is its half-life

A: Follow the procedure given below.

Q: Let u = (1,2,3) and v = (2a,2a,a^2) Which of the following values of a ensures thatu and v are…

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Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

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Q: Find the smallest value of x for which the series Σ (x+101)" 2ln(n) n=2 is conditionally convergent.

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Q: Question 6 dx Evaluate the integral improper integral (2r – 1)3 A 1/9

A: Given: ∫-∞ 012x-13dx

Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

A:

Q: Find Inz3 dz

A: LetI=∫lnz3zdzLet z3=udifferentiate 3z2dz=duDivide 3z2 on both sidedz=du3z2dz=du3z2Divide z oboth…

Q: 15. S(x + 2)²dx

A: Solve the following

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 3 r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x0 sin 2x x2-16 2. lim r14 (Yx+5)-3

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Q: 5. Fill in the blank: For x, y ER. Equality in the Triangle inequality is satisfied, i.e. Ix+yl =…

A: x+y=x+ysquare on both the sides;(x+y)2=(x+y)2 x2+2xy+y2 =x2 +2xy+y22xy=2xyxy=xyis true only…

Q: A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec. Assuming…

A: Let's find.

Q: f(x) ニ 9-3х A. x =-1 B. x = 0 C. x = 3 S2x x < 6

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Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

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Q: Express the repeating decimal as the ratio of two integers. 0.3 = 0.3333. The ratio of two integers…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8

A: Given,            rt=t2-8i+tj ; t=8To find : Tt and Nt at the given point.We know that,…

Q: Jan paid Php 9,250 on a loan made 6 months before at 12% simple interest. Find the interest…

A: Amount Paid after 6 months= 9250 rate of interest=12%=0.12 Recall: Amount after time t years…

Q: Find the volume generated by revolving the area bounded by parabolas y? = x and y = x² about x = -1.…

A: Given region is bounded by paraboal y2=x  and x2=y