Evaluate the following limit using Taylor series. 3 22²/2 (-) lim 2x² 848

Q: Find the critical numbers of the function f(x) = -x55x¹ +5x³ answers to three decimal places. X = X…

A: Given,            fx=-x5-5x4+5x3-9To find : Find the critical numbers of the function

Q: What is the gradient of f(x, y) = x² - y4 at the point (5, 2)? O 5i + 16j O -15i-16j O -6i + 13j O…

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Q: Answer the following questions for the function f(x)=x√√x² +9 defined on the interval -7 ≤ x ≤ 4.…

A: Concept: Concavity: Assume that f(x) is differentiable on interval I. If f′(x) is growing, the f(x)…

Q: Find the area of the region inside the inner loop of the limaçon r= 1 + 2 cos 0.

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Q: Let y Ay - 5x² + 8x + 4. If Ax = 0.4 at x = 5, use linear approximation to estimate Ay I Submit…

A: We know that ∆y=f(x+∆x)-f(x). So,             ∆y=f(x+∆x)-f(x)      =f(5+0.4)-f(5)      =5·…

Q: Find the gradient of the function f(x, y) = sin(x + 2y) O cos(x + 2y) [2î+î] cos(x + 2y) [i+1] O…

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Q: The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial…

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Q: The age of an ancient artifact can be determined by the amount of radioactive carbon-14 remaining in…

A: Here the age A (in years) is given by, A=-8267lnDD0 It is given that the amount D of carbon-14 that…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $43…

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Q: 3. Determine the point(s) where the function y = ₁ , has a maximimum and/or a minimum. Find BOTH…

A: Determine the point(s) where the function below has a maximimum and/or a minimum. Find BOTH…

Q: Find the constants a and b such that the function is continuous on the entire real line. 7₁ ax+b,…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x + 11 between x =…

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Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

Q: Find the average value of the function over the given interval. F(x) = = 2₁ [4, 6]

A: We have to find the average value

Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.

Q: 1. A) Express 0 1 4 1+x dx as a power series.

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Q: a) z=x² In (x y²) b) z=4 cos(x-3y)

A: As we know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…

Q: 7. Evaluate I = S ads, where S is the part of the plane x+y+z = a lying in the first octant.

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Q: 6. Use an integrating factor to solve the following first order differential equation (x² + 1) + xy…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Match each of the following parametric Equations with a plane curve : x(t) = - 3t y(t) = 1 - 9t² TER…

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Q: 14. The solution of the differential equation: (D - 2)³y = e²x is k a) y = (₁ + C₂x)e²x + xe²x b) y…

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Q: Use substitution method and find the indefinite integral Adx

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Q: Find the average rate of change of the function over the given interval. f(t) = 2t² - 5, [3, 3.1]…

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Q: dy Find for dx X 0 12+ 13t² dt.

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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 in terms of i,j and k

Q: Answer true or false. If £{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). True O…

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Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

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Q: = Let f be a function defined for t≥ 0. Then the integral L{f(t)} . - fotº e- 0 provided that the…

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Q: For an arithmetic sequence, a17 a1 = the sum of the first 65 terms= > Next Question - 47. If the…

A: It is given that, a17=47 and common difference(d)=5 a1=? Sum of the first 65 terms=?

Q: Determine whether the equation is exact. If it is exact, find the solution. (e'siny + 3y)dx -…

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Q: Applying Lagrange Multiplier, what is the minimum value of f(x, y) = x² + y2 where x > 0 and y> 0…

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Q: xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve…

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Q: (x-2y) dx + (2x+y)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

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Q: For the function f(x) = 3x2 −x3 − 4 where −3 ≤ x ≤ 3, complete the following. 12. State the values…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

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Q: Find the derivative of the function. q= 5 3 x + 6x

A: The given function q=x3+6x5

Q: n=1 n²2n-1 (-5)n

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Q: (a) ах = Du DE = du, ada voa waye by oz + + + 2x DE 2. (x²= y² + x) x (2x+₁) + (-2xy-9)x (-2y) (2x +…

A: We have to simplify (x2 - y2 + x) × (2x + 1) + (-2xy - y) × (-2y)

Q: Which of the following is the vector projection of (1, 0, 1) onto (-2,4,0)? 1 B. (-1,2,0) C.…

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Q: Find lim a. lim x→0* c. lim x²- - 5x + 6 2 3 x - 3x x -5x+6 b. lim x+3+ x³-3x² 2 x -5x+6 x³ - 3x² X…

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Q: Screenshot (168 Screenshot (168 Determine whether the differential equation (2x² − 2xy + 3) dx +…

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Q: How long will it take for an investment of $3,000 to double in value if the interest rate is 6.5%…

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Q: xydx + (x^2+y^2)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: Please see the below picture  detailed solution.

Q: Answer ise. The function f(t) = (et)10 is of exponential order. True False

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Q: 9 Given f(x): = =, find f'(x) using the limit definition of the derivative. x f'(x)=

A: The given function is fx=9x

Q: A population of 400 bacteria is introduced into a culture and grows in number according to the…

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Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. True False

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Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Break the limits according to f(t)

Q: 22) A- Find the distance between the line (y=x+3) and center of circle (x²+y²-2x=0). B- Using…

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