Perform the following integration. 1. (sinhæ)(coth? a+csch® a) dự sec³ x tan x 2. S dx √2 + sec x 3. S* (13² − 1| + |3² - 31) de x-1 4./²+²+8 dx 2.2 + 5x + 8

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A: Using substitution Z=y^n, and n=1/3 We get the linear differential equation

Q: Find the area bounded by y = 2 - x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE A D E

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Q: Answer

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Q: What is the y-coordinate of the centroid of the plane region bounded by y = x^3 and y=x^2? O 2/5 3/5…

A: We can solve this as follows:

Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: F T M 3. Let et = 2 . Find a power series nào ng t² a) Find a power series for te . obtained in @)…

A: We want to evaluate the power series of the given expression and want to integrate it.

Q: 1. Evaluate the following limits x-tanx 1. lim x-sinx x-0 9

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Q: 1-coth² (log₂x) dx x cosh(log₂x) 1. 11/20

A: We have to find the integral.

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

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A: The objective is to find the volume.

Q: The function f(x) = 900 represents the rate of flow of money in dollars per year. Assume a 10-year…

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Q: Perform the integration. (sinh x)(coth? x + csch3x) dx

A: Here is the solution:

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A: We have to find

Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

Q: Definition of first order, explicit ODE and the definition of it s solution.

A: Solution

Q: Sketch the graph of y = x-2 (x+3)²

A: The horizontal asymptotes by comparing the degrees of the numerator and denominator. Vertical…

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A: We have to find the marginal profit.

Q: IV. Solve the following problems completely. 3 1. Use local linear approximation to estimate √√(3.…

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Q: Use local linear approximation to estimate In (√0.99)

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: Find the absolute extremum points of f(x) = sin2 x + cos x on the interval [0, π].

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Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

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Q: VI. Determine the instantaneous rate of change of the functio: sin (³) f(x) = V² siz r³ 1 + √t at x…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = 2x + 1, x-axis,…

A: Given :y=2x + 1, x- axis, x=1, and x=2 is revolved about y=0.Formula :Volume in cubic = π∫y2 dy

Q: etermine the instantaneous rate of change of the function πt √√x sin (772³) dt : x = 1. x3 1 + √t

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: A rock thrown vertically upward at a velocity of 24 m/sec reaches a height of s(t) = 24t - 0.8t…

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Q: The integral of 3^4x dx is equal to * O 4^4x / In3 + C O 3^4x/In12 + C O 3^4x / In27 + C O 3^4x /…

A: SOLUTION-

Q: Stan 3x sec 3x dx 3.

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Q: Solve the differential equation of order one.  (x4 + 2y)dx - xdy=0 STEPS: a. Put the equation in…

A: Separate the equation to form standard form then solve

Q: Compute ff 24xyd A where R is the region bounded by R x = 1, x = 2, y = x, y = x².

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Q: 1 - cosh x lim x→0+ ln(x² + 1)

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Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

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Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x)(sin x- x-1) x+2+

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Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: Jill burns 100 calories per hour while sleeping, 300 calories per hour while walking, and 200…

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Q: -2 Given f(x) = ²√4 - t² dt, evaluate the following. -2 (i) f (-1) (ii) f(0), by interpreting f (0)…

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Q: If F(x) = = [₂√₂ x² a. F'(1) b. F(2), by interpreting F(2) as an area √4t - t² dt, evaluate the…

A: Given: F(x)=∫x20 4t−t2dt To find : F'(1) and F(2)

Q: 1. -3 Given that 9+x² following functions: (−1)n+1 Σn=0 32n+1 1. f(x) = 5 arctan x2n. Obtain the…

A: We have to obtain power series representation.

Q: Scot³ x ( cz) ¹4 dx sec x tan x 5.

A: Follow the procedure given below.

Q: Sketch the graph of r = 0 90° +2

A: To sketch the graph of r=θ90°+2.

Q: What is the y=x^2 - 4 and O 1/2 -1/2 3/2 -3/2 ONA y-coordinate of the centroid of the plane region…

A: Let's find y co-ordinate of the centroid of the plane bounded by two curves.

Q: C. Find the slope and the equation of the tangent line to the curve. 21: y=x²-4x+1 at (2, -3)

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Evaluate S2² (2x + 3e* − ¹) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given :∫122x+3ex-4xdx

Q: 5 Evaluate F.ds over the surface S defined by x² + y² + z² = 4 for z ≥ 0 and bounded by x = 0, y =…

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Q: For the function f(x,y) = 3 x³ + 5y4 5 4 x +y find f, fy, f(-1,1), and f,(-3,2).

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Q: Evaluate the multiple integral. * 131-x² SS S dz dy dx 100 0 2/3 5/3 4/3

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t² -…

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