Evaluate the definite integral. */4 sin(t) cos² (t) 6. dt

Q: Let U be the universal set of natural numbers less than 11. Consider the following two sets. A = {7,…

A: NOTE: Refresh your page if you can't see any equations. . U be the universal set of natural…

Q: Find the general solution of each of the following. rdp-(p+√pr)dr=0

A: Our Aim is to find the general solution of the following given below:-rdp-p+prdr=0 -(i)

Q: 2) Suppose that f(3) = 2.5, g (3) = 5, f' (5) = 2.7, f' (3) = 6.2, g (3) = -4, and g' (2.5) = 8. Let…

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Q: Let F(x, y) = 1 + √√1 − y². 1. Evaluate F(3, 1). Answer: F(3, 1) = 1 2. What is the range of F(x,…

A: Let's solve for function value at given point and its range.

Q: Find the equation of the tangent line to the curve at the given point (4,57) y= x3-2x+1

A: Tangent line of a curve y=f(x) at a point (a,b) is given by, y-b=f'(a)(x-a) Where f'(a) is the slope…

Q: Consider the improper integral [²8 8 + cos(0) 0² Determine if the improper integral converges or…

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Q: Find the integrals: 1- xdx A. -2/3 (1-x)3/2 B. 2/3 (1-x)3/2 + C C. -2/3 (1-x)3/2 + C D. -2/3…

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Q: Assume x and y are differentiable functions of t, related by the equation: x2+xy-y2=-31 If x = -3,…

A: Given x2+xy-y2=-31   ....1 and dydt=-1x=-3y=5

Q: Without using a calculator, compute the sine and cosine of 300∘300∘ by using the reference angle.…

A: Given angle:- θ=300°

Q: 1. Determine the domain and range of f(x) = 5

A: The domain of the polynomial function, fx=a0+a1x+a2x2+....+anxn is always a real number. Where n∈N…

Q: 2)Find an equation of the circle whose center lies in the second quadrant, that has radius 2, and…

A: We know that in second quadrant x-co ordinate is negative and Y- co-ordinate is positive. Required…

Q: Solve the given differential equation (2x + 4y - 1) dx (x +2y-3) dy = 0 Ox-3y-In (x+2y-3) = C O 2…

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Q: Given s(t) = 3t² + 3t, where s(t) is in feet and t is in seconds, find each of the following. a)…

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Q: Find a general solution to the differential equation: dx/dt = = x + e^t -- please show all work in…

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Q: Find fogo h. Chec fogoh = f(x) = 9x - 2 g(x) = sin x h(x) = x²

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: v = fb an V (x − 3)(x x= y₁²³-4y+3 чуте x = 3 X b 2₁₁ × [ f(x)] dx 29 x= 1x 2 y

A: v=2π∫13y(1+(y-2)2dy v=2π∫13y(1+y2-4y+4)dyv=2π∫13(y+y3-4y2+4y)dy

Q: (1.1) Calculate the Laplace transform of the following function from first principles: f(t) = = 3t -…

A: Laplace transform of a function f(t)  using first principles is Fs=Lft=∫0∞e-stf(t)dt

Q: f(x) || { -४४० -122 X ++ x + 2 C if x # -2 (and x = 0) if x = -2

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Q: (a) How long will it take an investment to double in value if the interest rate is 4% compounded…

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Q: 2. Circle the function if it is exponential, or if it is a transformation of an exponential…

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Q: 1. Find the solution of the IVP ty' = y +t³ sin(2t) – t³, y(t) = 3/t¹.

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Q: 1. 7. What is mos(+h)- cos(2), ? h (A)-1 (B) - √2 2 (C) 0 (D) 1 (E) The limit does not exist. 2 If…

A: 1 limh→0 (cos(π/2 +h) -cos(π/2))/h limh→0 sinh/h - 0 this is formula so answer  = 1 answer D is…

Q: Consider the graph below of the function g(x) to evaluate the integrals The graph consists of two…

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Q: Determine if the improper integral converges or diverges. 00 1 e2t + 8 S converges O diverges dt

A: Concept: Improper integral: An infinite limit of integration: If f(x) is continuous on [a,∞), then…

Q: dy Write the function below in the form y=f(u) and u = g(x). Then find as a function of x. dx y = -…

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Q: An oil storage tank can be described as the volume generated by revolving the area bounded by 2 y =…

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Q: f (x, y)=√x-2+√y-1

A: The objective is to find and and sketch the domain of the function.

Q: 하금 Find au du dx and 좀 하 dy (a) yuand u = x2 +2 dy (b) y = us and u = 4x2-x + 6

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Q: Sketch a quadric surface that could have the traces shown. Traces in x = k O k = ±2 k=+1 k=0 Traces…

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Q: (b) dy 3-4012 4xy + by2 ; dz = (1) y(1) = -1

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Q: Suppose that f is continuous on [0, 6] and that the only solutions of the equation f(x) = 3 are x =…

A: f is continuous on [0,6] and that the only solution of the equation f(x)=3 are x=1 and x=5.If f(4)=5…

Q: f(x)=5sin(2x) - 2x² - 4x Find the maximum or the minimum of the function using newton's method of…

A: Newton's method of optimization is the general method for finding the minima or maxima of the given…

Q: Draw the region of integration and reverse the order of integration to So evaluate the integral. 0 1…

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Q: 3) A university has 10 lecture halls. Each lecture hall has 15 rows of desks supo de With 5 desks in…

A: totak lecture halls=15

Q: the limit is positive or negative infinity. If the limit does not exist as a finite number or as…

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Q: 4

A: Concept: Given: Demand for the education: P=75-Q Supply for the education: P=2Q Due to decrease in…

Q: 2. Let us consider the given statement ~p ^ ~q The truth table of the statement is PT T LL FL q T F…

A: We have to write the final result of the table in words that too in a simple way to understand.

Q: = f(x) to 3) Use the appropriate integral formula for the length of a curve represented by a…

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Q: 1) Use the equation y = f(x) from part 1) and solve for x = g(y) as a function of y. = f(x)=7x=49…

A: We have to use the equation y=f(x) and solve for x=g(y) then we have to find L

Q: Find the PS of y' 2 cos²x - sin² x + y² 2 cos x y(0) = 1984

A: Given y'=2cos2x-sin2x+y22cosx and y0=1984

Q: below. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit doe

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Q: Evaluate I si sin³(x) cos³(x) dx .

A: We have to evaluate  ∫sin5x cos3x dx.

Q: Solved the following set of equations 16x +2y-2z = 16 2x 14y + 4z = -8 4x + 2y + 18z = 24 Using…

A: Find your answer, I solved using Jacobi method, upto 4 iterration

Q: T = 7/24 31nx - secydx - 5xsin ydy=0;y (e ³) : .

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Q: The the following 14 (sec) S (Ft) 0.4 1.5 3.56.29.6 positions s of a car at time table 0.2.4 0.6 0.8…

A: Concept: The average velocity is average velocity=∆s∆t=s2-s1t2-t1Instantaneous velocity=st.....(at t…

Q: (d) s

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Q: The graph of f is given. State the numbers at which f is not differentiable. (Enter your answers as…

A: Note:  1. A function is not differentiable at discontinuity. 2.A function is not differentiable at…

Q: x² - y² = 25, x ≥ 0, y = −5, y = 51

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Q: Evaluate the expression 3-³6².

A: Given, 3-362

Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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