1. Given the function f(x)=2-4x+ +$. Please find the intervals of increase or decrease, absolute maximum and minimum values the intervals of concavity and the inflection points.

Q: (d) Find the mass of lamina enclosed by y = ax² and y = c if the density of lamina d = xy a-2 c-6…

A: Let's find mass of lamina(m).

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number cubed and…

A:

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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Q: 6. Evaluate the following limits: 1/3 (x+8) -2 a. lim X x-0 b. lim x→-3 2 x²-9 2x² +7x+3

A: Given :limx→0x+813-2xlimx→-3x2-92x2+7x+3

Q: f(x csc² 6x-x cos 6x)dx

A:

Q: 25- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

A: Above question is solved.

Q: Determine the area to the left of x = 3- y² and to the right of x = -1

A: See the details solution in below

Q: 1) a) Find all vectors such that X = b) Explain why there is no such that X =

A: Solution: a) let v = (a, b, c). Then

Q: Calculate Differentiate. 1 = 2 z² + 1 f(z)

A:

Q: 5. Let f be a function continuous on R and F(x) = af f(t)dt. Then F"(0) is equal to 0 0 O f(0) ○…

A: Let f be a function continuous on R and Fx=x∫0xft dt. Then to determine the expression for F''0.

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 36 that lies above the plane z =…

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Q: Consider the region R bounded by y = Arctanx, x = 1, and the x -axis. Suppose that R has its…

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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: 10 5 Let A 4 1 -3 k 6-2 Find the values of k for which A is invertible. O Ais invertible ifk # 27.2.…

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Q: The inverse Laplace transform of H(s) = + (t) ==²e²+e-²t 8 1 " (3s+2)(S-2) b) f(t) ==e+e-2t -3 d)f…

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Q: Consider the region bounded by y = ex+1, ¹, y = 1, and y-axis.

A: Follow the procedure given below.

Q: Which of the following equations is(are) true? 1 S xdx lim = ( Σ 2+ =1 1 I xdx = - 2 + -2 O None of…

A: Above question is solved.

Q: 4 5 5 Let A = -1 -1 0 4 6 Use determinants to decide whether the matrix is invertible. Enter the…

A:

Q: V X if x 3 Find each of the following limits, if they exist. If a limit does not exist, answer…

A:

Q: ax x(x² - 1)

A: The given integral,       ∫dxxx2-1

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: Calculate √√3 8 2 1/√3 1 + x² dx

A: Given ∫13381+x2 dxTo evaluate the integral:

Q: Which of the following definite integrals gives the length of the arc y - 1 + 16x-dy 0 16y – 15 이 0…

A:

Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: To solve the following problem.

Q: Evaluate using Partial Fraction Decomposition: S x² (x+1)²(x-1) dx

A:

Q: 50lve the first order ODE UA x'sint - x Cost = -1

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Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

Q: Q6. Verify 02 f exDy Dyx for the function f(x, y) = x² sin2y + y²sin2x

A: A detailed solution is given below.

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A:

Q: What is the anticlockwise moment acting on this crane? 25 m 5m load M20000 N 4000 N movable-…

A: Above question is solved

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: Question 2 Find two numbers whose sum is "a", if the product of one by the cube of the other is to…

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

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Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

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Q: quickly

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Q: Solve for y esec(4y²-6y+14) = 3x + 1

A: To find the value of y , first, we take the logarithm on both sides of the given equation and then…

Q: independent

A: We will solve the problem.

Q: Evaluate using Partial Fraction Decomposition: x² (x+1)²(x-1) -dx

A:

Q: 4. Given f'(1) = 4, g'(1) =— 2, ƒ(1) = 1, g(1) = 1, find h'(1) if h(x) = xg(x)+7 f(x)

A: Using definition if derivative of f/g

Q: A wall lamp is positioned 7ft up a wall. A 6ft tall woman walks directly towards the light at a…

A: We need to find rate of shadow moving.

Q: ng the problem) an interval in which the solution of the given initial value proble (t-4)y' + (Int)y…

A: We have to find the interval of t

Q: 2 sin6 x cos⁹ x dx 0

A: See the details solution in below

Q: Solve the following integrals: 1. f-7e*dx 2. (2ex-6x) dx √(3¹) dx 3. 4. f 8x+1dx 5. f=dx X 6.…

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Q: (3x² - 10)dx x² - 4x + 4

A: The integral using substitution is answered below:

Q: (c) S x+4 x²+5x-6 2 dx

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Q: the argument of the Complex number: Z= ¹+√ √B-j

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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: Solve the integral shown below. JT fsins 2x cos7 2xdx

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Q: The x-component of a force of 50N is 30N, then what will be the y- component of the same applied…

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Q: Calculate lim X10 3x²-x-2 5x² + 4x + 1

A: