C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

Q: Consider the region depicted in the following figure. Find the area of R. -1 YA 4- 3+ 2 1 0 -1. f(x)…

A:

Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: Given :lnx-y=xy+y3y=tan3cot7x

Q: what about part (b) please.

A:

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³ ; (4) y = x sinh 2x -cosh 2x (2) y…

A: We need to find derivative. As per Bartleby's guidelines we can solve one question from multiple…

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

A:

Q: 2. Evaluate the following: t² dt a.

A: To solve: ∫−11 t2t2−62dt Let I = ∫−11 t2t2−62dt since,  t2t2−62 is an even function  Therefore, I =…

Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + s)i + j K = (No…

A: The given problem is solved below in detail.

Q: Ỉ Ỉ y=0 x=0 (r’–6xy® +5y*) dxdy =

A: Given, ∫02∫03x2-6xy3+5y4dxdy

Q: Use the substitution u= x² + 6 to find the following indefinite integral. Check your answer by…

A: To evaluate the integral.

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k ;

A:

Q: Use partial fractions to find the power series of the function: n=0 4x + 41 (x − 2)(x + 5)

A: To find power series for the given function.

Q: 1. y = Arccos 1-x

A:

Q: Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) limal; (2) Itm X(tan-¹x-x)

A: I have solved step by step in detail...go through the solution

Q: H.W: Evaluate the integral 1. 30 [ (x²y - 2xy)dydx 0-2

A: Given: ∫03∫-20x2y-2xydydx

Q: [3 37 tan5 x sec4 xdx Х

A: Given:

Q: Find the indefinite integral. (Use c for the constant of integration.) (2ti + j + 9k) dt 2ti + tj +…

A:

Q: Find the unit tangent vector T(t). r(t) = t²i + tj +4k, P(9, 3, 4) TO) (No Docpopcol

A:

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) 02 dx ; u nein!! sin x+cos x (2) […

A: We have to calculate the given indefinite integral according to the given information

Q: Evaluate the following limit. t sinj+ sin = 1+ k t -k π lim costi-5 1-x

A:

Q: At least one of the answers above is NOT correct. where a 9 and b = 7 1³h 10x² - [ 1(a) dx = f* f(x)…

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Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

A:

Q: (C): It w = tan x and x = 4t³¹ +t: Find d?

A: Given that w=tanx  and x=4t3+t. We have to find dwdt. We can write,  dwdt= dwdxdxdt  [ using chain…

Q: The volume of the solid obtained by rotating the region enclosed by x = 0, y = 1, x = y5 bout the…

A:

Q: dw (C): If w = tan x and x = 4t³ +t; Find dt

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

A:

Q: s 32x² (x-15) (x+5)² dx I

A: Integral

Q: If the L[ eatsin3t ] = a/( s² + bs + 42), determine the value of b.

A:

Q: Use the tabulated values of f to evaluate the left and right Riemann sums for n = 10 over the…

A:

Q: Given f(x) = - 12√x + fractions. f'(x) = The domain of f'(x) is 20 X 18, find f'(x) and its domain…

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Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: Given that, the position vector is rt=3t,4cost,4sint. Obtain the velocity.…

Q: dw (C): If w = tan x and x = 4t³ + t ; Find dt

A:

Q: Which of the following statements is (are) false? A) A basis is a spanning set that is as large as…

A: Please see the below picture for detailed solution.

Q: P 3. Evaluate the integral fx cos(3x²) dx as an infinite series. (You do not need to find the radius…

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Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

A:

Q: The after price tax on your new shiny car is $25,989.60. If a 4% sales tax was charged what was the…

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Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0

A: I am attaching image so that you understand each and every step.

Q: Find its length over the given interval. (Round your answer to four decimal places.) (No Response)

A:

Q: 04: Answer two only: (A): I A-2 1 -1 1-2 Find AB and AC.. -- 3 1 1 and 1 3 1 CO

A: Given :A=420210-2-11, B2312-2-2-121, C=31-3026-121

Q: -9 (x-1) 8. √x dx

A:

Q: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: To find derivative.

Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

Q: 61. A "bead" is formed by removing a cylinder of radius r from the center of a sphere of radius R…

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Q: 2-x Evaluate: 44-3 dx A. In 4x² + 4x-31+ In 2+ 8. In 4x² + 4x-31+In+C c. In 4x² + 4x-31+In++C D. In…

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Q: The answer above is NOT correct. Find the area of the region enclosed between y = 4 sin(x) and y = 3…

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Q: Given F(x) below, find F'(x). Provide your answer below: F(x) = I 4 (414 + sin* (t)) dt

A: