I need a step-by-step solution, please 2 bn=² ST T S™ sin x sin nx dx

Q: d the equation of the tangent line to the curve y = 5x cos x at the point (7, e equation of this…

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Q: Solve the differential equation (2x + y) dx (4x + 2y − 1) dy = 0 O a. 5x 10y + In 10x 5y 2|= C O b.…

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Q: Find two positive numbers that satisfy the given requirements. The second number is the reciprocal…

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Q: 5) Calculate the area of the region between the curves: y = 2 = x² and y = x²

A: We can find the area as below.

Q: 52. y' - y = y³

A: We need to solve D.E.

Q: Calculate r' (t) and T(t), where T'(t) = ( T(t) = { r(t) = (8+t, (9+t), 2+2t). ).

A: Given vector function r(t)=8+t, -9-t, 2+2t

Q: 5) Calculate the area of the region between the curves: y=2-x² and y=x²

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Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: Write an equation of the form y = mx + b for the line in the following graph. [Hint: Either find the…

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Q: If the vector equation of a line is 7=(3, -5)+t(-2, 3), t€ R. the parametric equations are Ox=3-2t,…

A: Topic:- application of geometry

Q: Question 13 (1 point) ✓ Saved Which of the following CANNOT be an acceptable direction vector for…

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Q: Calculate each of the following given that: a. b. a-b a x (2b - 3c) |b x 3c| C. d. projac a = 2i -…

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Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: 2y dx + x(x² In y − 1) dy = 0.

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Q: 4 sin(x - 2) x→2 3 ln (3x – 5) Evaluate lim and write your answer in simplest form.

A: We can find the limit in the following steps.

Q: Explain why the integral is an improper integral and evaluate it: =dx √x-2

A: Given integral:- ∫251x-2dx

Q: lve y' = 14xy – 2x, y(0) = 11 x) =

A: Topic:- application of integration

Q: ∞ 1.00 8e- dx = (If the integral diverges to ∞ or -∞, type oo or -oo; if the integral diverges in…

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Q: Determine the solution of the following differential equation: d²y dx² dy -8-+16y=0 dx where y(0) =…

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Q: dv/du = (uv)² — 2(u — v) — 2.

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Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

Q: Express a = the limit lim Σ(4(x*)² – 3(x* )³) Aï; over [6, 7] as an integral. n→∞ i=1 Provide a, b…

A: The given limit limn→∞∑i=1∞4xi*2-3xi*3∆xi over the interval 6,7

Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy dx 3 +…

A: We have given differential equation  dydx=3+18xxy2 y2dy=3+18xxdx Integrating both sides…

Q: Find the inflexion point(s) of f(x) = x²-3x²³

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Q: QUESTION 10 Use cylindrical coordinates to evaluate the integral below. √x² + y²dv, where E is the…

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Q: The graph below is the function f(x) Find lim Find lim I→-1- Find lim 4 3 I→-1+ in 2 01 I-1 es 1 2…

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Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: 3 3 3 2 (49) (+91 i- -74+ i n n n integral, that is provide a, b and f(x) in the expression f(x)dx.…

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Q: J 1 cot³ x O 3 2 dx = In | sec² x − 1| + C --- O 1 tan² x + ln | sec x + C 4 O 1 2 O 1 2 1…

A: I have stated the used formulas in the solution

Q: Consider the graph of f. f(z)dz (2) The shaded region over [0, 7] has an area of 314 and evaluate…

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Q: y 3 2 1 -1 -2 -3 -4 1 2 3 4 5 6 X

A: We can find the Domain and Range of the function.

Q: If the substitution y = x is made, the integral - 1 64 2 3x³ 3+x² 3x³ 3 + x² .64 18x8 3 + x² S™ [²3…

A: The objective of the question is rewrite the integral  and choose the correct option.

Q: solved

A: Please refer to the image below

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that ƒ(3) = 9, ƒ(9) = 2, ƒ'(9) = 15, ƒ'(3) = 13…

A: Given Fx=ffx Gx=Fx2 f3=9, f9=2, f'9=15 and f'3=13

Q: 7 Find the area under the curve y = x over the interval [1, 5]

A: Please refer to the image below

Q: у 3 2 1 -1- -2 -3 1 2 3 4 5 6 X

A: Here is the solution:

Q: Find the derivative of ( Ⓒ) (05'(x)

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Q: Evaluate the integral using the following values. [x³ dx = 260, x 29 - ·[³x dx = 10, [³dx = 2 (29 -…

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Q: (4) (d) 2-7 dx 4x-2 x²-1 (4) (e) S 7x (4x²+5)3 dx

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Q: 12. Given the vector equation [x, y]= [3,1]+[3,-5] find a) the parametric equations b) the symmetric…

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Q: 49. y' + (-) x =) = xy²

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Q: A stone is thrown straight up from the edge of a roof, 875 feet above the ground, at a speed of 14…

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Q: Consider the function f(x) = 6x¹0+ 3x5 - 2x³ - 3. An antiderivative of f(x) is F(x) A is and n is…

A: The given function fx=6x10+3x5-2x3-3 use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C

Q: (1+x²)y' + 2xy = (1+x²)y

A: Given problem:- 1+x2y'+2xy=11+x2y

Q: If what does the following integral equal? - 11 [¯¯1² [8f(x) + 2g(x) — h(x)]dæ = - 68 - 11 [= f(x)…

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Q: Use the graph of the function f(x) shown below in order to determine all values of a in the interval…

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Q: -6-5-4-3-2-1 6 I 4 3 2 L -2 -4 -5 T 2 3 4 5 6 X

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Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

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Q: Write the interval in set notation. [2, 6) {x | 2 < x ≤ 6} {x | 2 ≤ x < 6}   {x | 2 ≤ x ≤ 6} {x | 2…

A: Write the interval in set notation. [2, 6) {x | 2 &lt; x ≤ 6} {x | 2 ≤ x &lt; 6}   {x | 2 ≤ x ≤ 6}…

Q: 1. (x³ + xy²)y' = y³ Ssangen job10 2. (2x + y)dx= xdy 3. x³y' + x²y-y²= 2x4

A: Topic:- differential equation     Definition:- The order of a differential equation is defined to be…