Using the Maclaurin series expansion of e, to find the series expansion of f(x). Express [ f(t) dt as an infinite series. Use (ii.) to approximate [ f(x) da to within an error of 0.01.

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Q: 1) dx x²+3x-4

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Q: J (11x + 17) dx 2x² + 7x - 4

A: We have to find Integration of given Integral.

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Q: al

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A: Above question is solved

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A: Consider the integral  ∫tan2x dx

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Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

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Q: Complete the parametric equations of the line through the point (-2,-4,-8) and perpendicular to the…

A: Given: Equation of plane x-3y-5z=2 Point (-2,-4,-8)

Q: III. Consider the parabola C: 2 - 4 = -(x - 2)² on the zz-plane. 1. Find the center-radius form of…

A: Given that Parabola C : z-4 = -x-22                In this question, we sketch a graph of the…

Q: √3 ♡ dx 1 + x2

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Q: Solve the integral shown below. So cos¹¹ 3xdx Só 11

A: ∫0π6cos113xdxLet u=3x.=∫0π2cos11u13du=13·∫0π2cos11udu=13·∫0π21-sin2u5cosuduLet…

Q: 5. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = X. 4 f(x)= = and g(x)…

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Q: * Two unlike parallel forces, each of magnitude 50 kN are 200 mm apart from each other. what will be…

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Q: To estimate the height of a building, two students find the angle of elevation from a point (at…

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Q: Determine the area below y = 3 + 2x - x² and above the x-axis

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny [the Low +¹Y2 ex+y dxdy 0

A: See the details solution in below

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Q: Find the limit or show that it does not exist. lim x - √x 818

A: follow next step

Q: Select the correct answer to the following problems: a) f(x) f(x) dx ○ f(4) 00 ○ f(0) f(x-4) f(x)dr…

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Q: - Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x) -1(y/x)

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Q: (2) Consider the function where a, b are constants. g(t) = if t 1

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Q: Solve the following system: 2x + y - 3z = -3 x + 3y - 4z = 11 x + 8y-9z = 5 (2,-1,0) no solution

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Q: KIN KIN 0 2 d2 sinr do dr dọ

A: A detailed solution is given below.

Q: C. r = a sin²0 3. r= a(1 + cose)

A: Topic:- curves  Note :- as per our guideline if more than three subparts posted than only first…

Q: Consider the following matrix. A = [22 -2] How many vectors are in the basis of row(A)?

A: Given: Now,                   30-3222Reduced matrix to reduced row echelon form:=10-1012The rank of…

Q: Q4- Solve the following differential equation: (1 + x²) dy + (y-tan-¹(x)) dx = 0

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Q: Given z=x²y+3xy4, x=sin(2t), y=cos(t), find dz/dt when t=0

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Q: The profit function of Company ABC for a specific product is given by y = x² - 6x² + 9x and 0≤x≤ 2.…

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Q: A box with square base and open top has a volume of 1000 m³. Find the dimensions of the box which…

A: This question can be solved using the concept of maxima and minima.

Q: (2x²9x9)dx x3 x³ - 9x

A: Here we have to do partial fraction and after that integration

Q: Let ā 47- 57 and b - 27 + 3j + 4k. Find - 2ā - 36.

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Q: A particle moves along a straight line such that its displacement at any time (t) is given by…

A: Note: There is a typo in the question.  Incorrect:  S = t^3 - 6t^3 + 3t +4   Correct:  S = t^3 -…

Q: Correlational designs have one independent variable and one dependent variable  true or false?

A: Explanation:-  A  dependent variable is the variable to be explained and independent variables are…

Q: If f(x) = 5³x then f'(x) = 5.A 5h 3 In S O 3x(5³-1) 5³ (In 125) 3(5²)

A: Here, the given function is: f(x)=53x So, note that ddx(ax)=axln(a) where a is a constant.

Q: dx √3 1 + x²

A: we use the  formula ∫dx1+x2 = tan-1 x    +C

Q: The vector a has a magnitude of 7. Its x component is 2, and its y component is twice its z…

A: Given: The vector 'a' has a magnitude of 7. Its x component is 2, and its y component is twice its z…

Q: Evaluate using Partial Fraction Decomposition: (y+1)²(y−1) dy f

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Q: 4. 5. 1 X√(x)}² (x)²-49 dx 1 √9+8x-x² dx

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