Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4 + 2arc(csc)

Q: B.) For numbers 1 to 10: Determine if limit of each function exist using the piece-wise function…

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Q: Which of the following is not true? 5 dx dx ® (Α Sº o 25-x² lim c+5-0 25-x² ® √ in(x²) dx = lim_…

A: We have determine the integration

Q: Solve the differential equation a. (4x³y² - 6x³y - 2x - 3)dx + (2x¹y-2x³)dy=0 b. (x-4y-3)…

A: If the differential equation Mdx +Ndy =0 is exact i.e, ∂M∂y=∂N∂x ,then solution is        ∫y…

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

A:

Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0≤x≤1

A: Area  of surface is obtained.

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: topic - application of derivatives

Q: 4 3. 2 1 -4 -3 -2 -1 2 -1- -2- -3+ 3. From the above graph of y = f(x), find the following limits:…

A: a)2  b) -2  c) -4

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: Given than han [ 1 (2) de = (z) dz=-4 and ® [1(e) de - [5 (2) de = 20 None of the given choices…

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Q: Find the area bounded by the parabolas (x-2)²-9py = 0 and y² = 9p(x-2).

A:

Q: State the domain, vertical asymptote, and end behavior of the function. g(x) = ln (6x + 12) + 1.3…

A: Domain of a function:-  Set of all values of independent variable such that function at that point…

Q: Find the area bounded by y = x3 +6, y = x and y-6 www. -X.

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Q: Find the length of the spiraling polar curve r = 6e50 From 0 to 2. The length is

A: SOLUTION-

Q: Given x = - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

A:

Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

A: Velocity of the particle is given by:vt=9sin 3πt

Q: Determine the Cartesian equation of the tangent line to C1 at the point where 0 = π/2. Given: polar…

A:

Q: Find the complete solution of ds dt = 5t* √√s.

A: Given problem:- Find the complete solution of dsdt = 5t4√s

Q: Jonathan invested $240,000 to purchase a home. After 14 years, he sold the home for $320,000.…

A: We have to find interest rate on the investment.

Q: Calculate the volume of the solid of revolution generated by rotating the graph of the following…

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Q: Determine whether the given 3-tuple (6, -2, 2) is a solution of the linear system: 2x₁-4x2-x3 = 2 x₁…

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Q: 3 So² √(√₁² - ²√₁²³) ²³ a dt

A:

Q: 1 Find the arclength of the curve x = 3 1 ',v = 22 -t³ t2 with 7 ≤ t ≤ 8.

A: The arc length of a curve in parametric form x=f(t) ; y=g(t) for b≤t≤a is given by,…

Q: ly If cosh x = then sinh x = Select one: True False If f is continuous on a closed interval, then f…

A:

Q: 2x²+x-2 (x + 1) (x²+1) dx = √ [+41 + x+ 2 If S A B 5 © €/ 5 D 4 E) None 5/2 B (2x) + C 1 x²+1 dx,…

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Q: The trough in the figure is to be made to the dimensions shown. Only the angle can be varied. What…

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Q: Find the limit of the following sequence that the limit does not exist- or determine. {(₁ + + )"}…

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Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. (a)…

A: Both integral is solved.

Q: . The area bounded by the parabola y² + x - 2y = 1, the x-axis, and the line x = 2 revolves about…

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Q: If you evaluate the integral expression Blank 1 Add your answer 12x + 1 dx the result is Blank 1…

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Q: L= dx= 1 -2 X 2x4 (A) True B) False | m 100

A: Use basic integration to evaluate definite integration.

Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t == . — = dt

A: Given:ds/dt=10csc^2(2t) To find: solution at s=2 and t=π/4

Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x² - X…

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Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 2.

A:

Q: e2-s L-1 (5(5²-53) O [(-1/3) + e^(4(t-1))/3] e^2 U(t-1) O [(-1/3) + e^(3(t-1))/3] e^2 U(t-1) O None…

A: We have to find the inverse Laplace transform of the above expression.

Q: Find (a) v xw, (b) wxv, (c) vxv, and (d) wxw. v = i + 3j, w = 2i + 2j + 3k (a) v xw= (Type your…

A: Given query is to find indicated vector operation.

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: Find f^-1(x) for f(x) = 9+8x f^-1(x) = ____

A: Topic = Function

Q: olve for the general solution using the Power Series. The answer was ready given, you just have to…

A: Please see the below picture for detailed solution.

Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

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Q: example of properties of definite integral

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Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all f'(c)…

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Q: Let z(t) = 5 cos(t) and y(t) = 3.sin(t) All answers should be decimals rounded to 2 decimal places.…

A: Given that,   xt=5.cost and yt=3.sint

Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

A: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. HI-4 (a) lim f(x)g(x) #114 (b) lim…

A: Given problem:-

Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A:

Q: Considering C is a curve which has the following parametric equations: 1 t³t+1, C = { x (t) = { 1³3…

A: Parametric equation