Find the determinant of the following elementary matrix by inspection. 10 0 0 01 0 0 E = 00-70 00 01 det(E)=

Q: X y = (sec x) log2 a

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Q: A car is moving with uniform acceleration. it covers 200 m in 2 sec and 220 m in next 4 sec. the…

A: A detailed solution is given below.

Q: √√3 L dx 1+x²

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Q: Use a Maclaurin series for sin x to obtain the Maclaurin series for f(x) = sin(x¹).

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Q: (c) S x+4 x²+5x-6 2 dx

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Q: Using the Maclaurin series expansion of e, to find the series expansion of f(x). Express [ f(t) dt…

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Q: Solve the integral shown below. . S | xsin xdx

A: Given problem:- ∫x sin(x)dx

Q: 7. f (ex + 1)² dx 8. fex dx/(e²x + 3) 9. f (cos x-sin x)² dx

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Q: 4dx 3 x - √√x² S

A: We will use simple Integration rules to solve this question.

Q: Problem 4. Find the second derivative of below functions. (1) f(x) = 4, (2) g(x) = ln(3x² + 2x - 5).

A: 1)f(x)=41/x 2)g(x)=ln(3x2+2x-5).

Q: find maximum and minimum of f(x)= 3x2+15x2-36x+10

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Q: (2x -۱۱۶ (3x44795

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Q: 4. Find the Taylor series for f(x) = ln(1 + x) centered at a = 3. Give the first 5 terms of the…

A: This is a problem related to taylor series expansion. Based on the general formula and concept we…

Q: 8 Determine the area of the region bounded by the curves y = =, y = 2x and x = 4

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Q: Integral Calculus

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Q: (5x-5)dx 3x² - 8x - 3

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Q: 6dx S: ³√x² x-

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Q: The angle between the vectors [√2 – 1, √2 + 1, √2] and [1, 1, 1] is: 45° 60° 90° 30°

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Q: f(x csc² 4x - x cos 4x)dx

A: The answer is given below:

Q: A particle is moving on a straight line with the acceleration and initial velocity a(t) = 2t - 2,…

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

A: To solve the following differential equation: 1+x2dy+y-tan-1xdx=0

Q: of the given conditions. lim f(x) = ∞, 210 Limits at Infinity - Horizontal Asymptotes Sketch the…

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Q: Find an equation of the line tangent to the curve tan¹(y) = (x+y)e at the point (0,0). tan ¹(xy) =…

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny [TD [t ex+y dxdy

A: Given problem:-

Q: Evaluate the following integrals by interpreting each in terms of areas. (²√₁ 1 - x² dx Jo

A: Recall:  Area of circle=πr2

Q: ve for y esec(4y²-6y+14) = 3x + 1

A: We have to solve for y of the given equation

Q: Determine if the improper integral •+∞ dx x ln7 x is convergent or divergent.

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Q: Find a power series representation for the function x f(x)= 9+x² and determine the radius of…

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Q: Hả+b+c = 0, show that ả x b = b xả = xã

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Q: Suppose f(x) = 3x² + x - 3x²+x-6. Compute the following: A.) ƒ( − 4) + ƒ(1) = = B.) f(-4)-f(1) =

A: Given f(x)=3x2+x-6f(-4)=3(-4)2+(-4)-6=3(16)-4-6=48-10∴f(-4)=38

Q: Q4. f(x)=5 and 1(x)de=8 dx = 5 and f(x) dx = 8 then f(x)dx a) -3 b) -13 c) 13 d) 3 dx is given by

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Q: Which of the following is equal to In 4 ? 4 offen O et dt 1 O ln 3 + ln 1 dt of - In 8 In 2 t

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Q: Which of the following statements is true about g(x) = 8 at x = 8? O g(r) is continuous at x = 8 O…

A: Consider the function  g(x)=x+8x-8

Q: Derivative app The given rectangle has a perimeter of 60cm. Find the values of x and y that result…

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Q: Use any method to determine whether the series converge. ∞ 1 (2) Σ 4k k=1 The series (5) Σ k=1 The…

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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: Show that lim in(+¹) + sin(+²) + n *** + sin(2) cos(1) - cos(2).

A: Above question is solved.

Q: Find the point at which the line x(t) y(t) z(t) - 5+ 5t -6-8t intersects the z plane. - 7+8t

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Q: Find dy dx G. y= = 20 In (e 5* +20) b. y = 20x (220x) c. y = €²0x-1 + 20 (n (ex)

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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: Q3- Sketch the region of integration and evaluate the integral: In8 Iny ["C ex+y dxdy

A: Given double integral ∫1ln8∫0lny ex+y dx dy

Q: the arclength of the curve y = on 3

A: We will solve the problem.

Q: dy For the following composite function, find an inner function u = g(x) and an outer function…

A: Given problem:- For the following composite function, find an inner function u = g(x) and an outer…

Q: False

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Q: Find the modulus and argument of (a) Z₁ = -√3+√ and (b) 2₂ = 4+ Y j Hence express Z₁ Z2 and 2₁/22 in…

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Q: Water is poured at a rate of 10 cubic meters per minute into a conical tank 6 meters across the top…

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Q: Solve the following. x³-x²-√2x limx→21 x2-11x+18

A: To evaluate the given limit, first, we multiply the numerator and denominator of the given function…

Q: 5: Evaluate I where D is the rigion bounded by xy ve x+y = 7 SS (X+Y) DA D (1

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Q: If f is continuous and ƒ(5) = 2 and ƒ(4) = 3 then lim ƒ(4x² – 11) = x→2 True False

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Q: x³-y³ Determine whether the function z = g(x, y) = x² + y² (why or why not) for for (x, y) = (0,0)…

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