Evaluate the integral using trigonometric substitution. 1 dx xV1 + x6

Q: First make a substitution and then use integration by parts to evaluate the integral 6 cos (Vx) dx.

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Q: sec x dx Vcot x 2.

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Q: 21. Find y' using implicit differentiation. a) In (xy + x + y) = 2 b) In (sin xy) = xy

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Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of a Norman win...

A: we should find the height of the rectangle such that the window will admit the most light.

Q: 25. Evaluate the following definite integrals. c) LIVII – x dx

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Q: Solve ſ cot3 4x csc² 4x dx then evaluate the answer at x=22, C=26

A: ∫cot34x csc24x dx

Q: Evaluate the indefinite integral sin (t)cos (t)dt

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Q: dy 4x+xy? dx

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Q: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

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Q: Eliminate ARBITRATY CONSTANTS y = a²t² ; x =b + at

A: Given:To Eliminate ARBITRATY CONSTANTS y = a²t² ; x =b + atSince  we know that, number of independen...

Q: The function f is shown below. What is the value of | f(z) )dx? Write your answer in simplest form. ...

A: Topic:- integration   

Q: Find the volume V of the described solid S. The base of S is the triangular region with vertices (0,...

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Q: 6 state if a power function. If so, write it in the form f(x) = kx". If not, type N for k and p For ...

A: To solve the following problem

Q: The form of the partial fraction decomposition of a rational function is given below. 16 – (x² + 10x...

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Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places acc...

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Q: 19. Differentiate the following functions. g) y = 2 h) y = xsin-1x+ V1- x2

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Q: For f(x, y) = 2x3 + x²y2 - 5y3 + 10,

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Q: about the y-axis

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Q: 19. Differentiate the following functions. e) f(z) = z? cos 2z + z sin (z?) f) y = In ( sec 2x + tan...

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Q: 28. Sketch the graph of 2x + 4y + 3z 12.

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Q: 1. Complete the given 2 sets of tables of values to investigate the limits of a function. lim a? – 5...

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Q: A. 2xydx + (y – x²) dy = 0 -

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Q: sec(Vx) tan(Vx) dx

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Q: A. (A +B+C+D+ E+ F) B. (P + Q +R+M + N) (x² + 1)(x + 1) (2x + 3)* dy or y': dx Ах' + Bx? + 2х + с Dx...

A: As per our guideline we are supposed to be answer only one question you can repost other questions i...

Q: Solve for the differential equation

A: Note: In the first question given equation is not clear as only left hand side of the equation is gi...

Q: Find the first and second derivatives of the function. g(t) = t°(6t + 5)* g'(t) g"(t) =

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Q: х+1 3. J 25 – x²)3/2

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Q: 1 d.r r/1+x°

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Q: Question 15 15. The first derivative of the logarithmic function f(x)= In (e +3) is 1 A e +3 B e +3 ...

A: Topic:- application of derivatives

Q: The Ideal gas law is given by the equation: pV = nRT where p = pressure, V = volume, n = number of m...

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Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the cu...

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Q: 7. If exactly 100 people will sign up for a local flight, the airline will change P 3,000.00 per per...

A: The given no. Of people is 100 and the charge is 3000 per person. If more than 100 people sign up, t...

Q: Question 3: Suppose that H = xy + V3x2 + 4y?, and at t = 0 (initiation) we have r = 1, y = 1, H = 6,...

A: Let's find. 

Q: Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate ...

A: Let ,Time = t P = $7,000 Rate = 7% = 0.07 P'(t) = dP/dt (a) Write a first-order linear differential ...

Q: Solve dy and Evaluate the answer at y=30 and C=-26

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Q: Graph of f 8. 7. 6. 5. 3. -10 -9 -8 7 -6 -5 -4 -3 -2 -1 3 4 5 8. 10 -1 -2 -3 -4 -5 -6 -8- 6.

A: Solution

Q: 24. Find the limit using the L'Hospital's Rule. a) lim x+0 (e2k-1) Inx b) lim X+0o x

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Q: Let us try to find where a function is increasing or decreasing given the following.  f(x) = x3−4x,...

A: Topic:- calculus

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: Use integration by parts to evaluate the definite integral. 8t? In(t)dt Give an exact answer

A:     ∫1e8t2lntdt=8·∫1et2lntdt=813t3lnt-3·∫t23dt1e=813t3lnt-3·t391e=813t3lnt-t331e=82e39+19=82e3+19

Q: ·를 sin' X V cos x

A: This question is related to definite integration, we will solve it using given information. 

Q: B. Odr + (2r +1- Or) d0 = 0

A: θdr+(2r+1-θr)dθ=0drdθ=θr-2r-1θdrdθ=r-2rθ-1θdrdθ=r(1-2θ)-1θdrdθ-r(1-2θ)=-1θdrdθ+(2θ-1)r=-1θ It is a l...

Q: The integral in this exercise converges. Evaluate the integral without using a table. 40 xp. x² - 25...

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Q: The graph of f', the derivative of f, is shown below. Determine all possible inferences that can be ...

A:   ---------------------------------------------------------------------------- Key points: If f'x  ...

Q: 3. TVI+ 1 dx (use trigonometric substitution

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Q: ifx 1

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Q: The graph of the function f is shown on the graph below. On the axes beneath, sketch a possible grap...

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Q: Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the functio...

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Q: 26. Find the area of the region bounded by the curve y = 4x – x?, the lines x = 1 and x = 3 and the ...

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